dynamics_analysis/highdim_CANN.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "db07ced9",
   "metadata": {
    "lines_to_next_cell": 0
   },
   "source": [
    "# Continuous-attractor Neural Network\n",
    "\n",
    "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/brainpy/examples/blob/main/dynamics_analysis/highdim_CANN.ipynb)\n",
    "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/brainpy/examples/blob/main/dynamics_analysis/highdim_CANN.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "18cc3597",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:03.297239800Z",
     "start_time": "2023-07-22T05:49:01.924476Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c371c71d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:03.998906400Z",
     "start_time": "2023-07-22T05:49:03.297239800Z"
    }
   },
   "outputs": [],
   "source": [
    "import brainpy as bp\n",
    "import brainpy.math as bm\n",
    "\n",
    "bm.set_platform('cpu')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "87267a8e2042e409",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:04.015020200Z",
     "start_time": "2023-07-22T05:49:03.998906400Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.4.3'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bp.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3ea7e0",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "db58c3dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:04.030655500Z",
     "start_time": "2023-07-22T05:49:04.015020200Z"
    }
   },
   "outputs": [],
   "source": [
    "class CANN1D(bp.dyn.NeuDyn):\n",
    "  def __init__(self, num, tau=1., k=8.1, a=0.5, A=10., J0=4.,\n",
    "               z_min=-bm.pi, z_max=bm.pi, **kwargs):\n",
    "    super().__init__(size=num, **kwargs)\n",
    "\n",
    "    # parameters\n",
    "    self.tau = tau  # The synaptic time constant\n",
    "    self.k = k  # Degree of the rescaled inhibition\n",
    "    self.a = a  # Half-width of the range of excitatory connections\n",
    "    self.A = A  # Magnitude of the external input\n",
    "    self.J0 = J0  # maximum connection value\n",
    "\n",
    "    # feature space\n",
    "    self.z_min = z_min\n",
    "    self.z_max = z_max\n",
    "    self.z_range = z_max - z_min\n",
    "    self.x = bm.linspace(z_min, z_max, num)  # The encoded feature values\n",
    "    self.rho = num / self.z_range  # The neural density\n",
    "    self.dx = self.z_range / num  # The stimulus density\n",
    "\n",
    "    # variables\n",
    "    self.u = bm.Variable(bm.zeros(num))\n",
    "    self.input = bm.Variable(bm.zeros(num))\n",
    "\n",
    "    # The connection matrix\n",
    "    self.conn_mat = self.make_conn(self.x)\n",
    "\n",
    "    # function\n",
    "    self.integral = bp.odeint(self.derivative)\n",
    "\n",
    "  def derivative(self, u, t, Iext):\n",
    "    r1 = bm.square(u)\n",
    "    r2 = 1.0 + self.k * bm.sum(r1)\n",
    "    r = r1 / r2\n",
    "    Irec = bm.dot(self.conn_mat, r)\n",
    "    du = (-u + Irec + Iext) / self.tau\n",
    "    return du\n",
    "\n",
    "  def dist(self, d):\n",
    "    d = bm.remainder(d, self.z_range)\n",
    "    d = bm.where(d > 0.5 * self.z_range, d - self.z_range, d)\n",
    "    return d\n",
    "\n",
    "  def make_conn(self, x):\n",
    "    assert bm.ndim(x) == 1\n",
    "    x_left = bm.reshape(x, (-1, 1))\n",
    "    x_right = bm.repeat(x.reshape((1, -1)), len(x), axis=0)\n",
    "    d = self.dist(x_left - x_right)\n",
    "    Jxx = self.J0 * bm.exp(-0.5 * bm.square(d / self.a)) / (bm.sqrt(2 * bm.pi) * self.a)\n",
    "    return Jxx\n",
    "\n",
    "  def get_stimulus_by_pos(self, pos):\n",
    "    return self.A * bm.exp(-0.25 * bm.square(self.dist(self.x - pos) / self.a))\n",
    "\n",
    "  def update(self):\n",
    "    self.u.value = self.integral(self.u, bp.share['t'], self.input, bp.share['dt'])\n",
    "    self.input[:] = 0."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "952c4240",
   "metadata": {},
   "source": [
    "## Find fixed points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d9eb1078",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:04.296285200Z",
     "start_time": "2023-07-22T05:49:04.030655500Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "model = CANN1D(num=512, k=0.1, A=30, a=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d5e87916",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:58.981342100Z",
     "start_time": "2023-07-22T05:49:04.296285200Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimizing with Adam(lr=ExponentialDecay(0.1, decay_steps=2, decay_rate=0.999), last_call=-1), beta1=0.9, beta2=0.999, eps=1e-08) to find fixed points:\n",
      "    Batches 1-200 in 1.05 sec, Training loss 0.0003816649\n",
      "    Batches 201-400 in 1.00 sec, Training loss 0.0000117727\n",
      "    Batches 401-600 in 1.07 sec, Training loss 0.0000027707\n",
      "    Batches 601-800 in 1.03 sec, Training loss 0.0000026347\n",
      "    Batches 801-1000 in 0.95 sec, Training loss 0.0000026309\n",
      "    Batches 1001-1200 in 1.01 sec, Training loss 0.0000026283\n",
      "    Batches 1201-1400 in 1.00 sec, Training loss 0.0000026258\n",
      "    Batches 1401-1600 in 1.00 sec, Training loss 0.0000026233\n",
      "    Batches 1601-1800 in 1.04 sec, Training loss 0.0000026209\n",
      "    Batches 1801-2000 in 0.97 sec, Training loss 0.0000026185\n",
      "    Batches 2001-2200 in 1.02 sec, Training loss 0.0000026162\n",
      "    Batches 2201-2400 in 0.98 sec, Training loss 0.0000026141\n",
      "    Batches 2401-2600 in 1.01 sec, Training loss 0.0000026120\n",
      "    Batches 2601-2800 in 1.05 sec, Training loss 0.0000026100\n",
      "    Batches 2801-3000 in 1.03 sec, Training loss 0.0000026081\n",
      "    Batches 3001-3200 in 0.97 sec, Training loss 0.0000026063\n",
      "    Batches 3201-3400 in 1.10 sec, Training loss 0.0000026047\n",
      "    Batches 3401-3600 in 1.06 sec, Training loss 0.0000026031\n",
      "    Batches 3601-3800 in 1.05 sec, Training loss 0.0000026016\n",
      "    Batches 3801-4000 in 1.13 sec, Training loss 0.0000026003\n",
      "    Batches 4001-4200 in 1.10 sec, Training loss 0.0000025990\n",
      "    Batches 4201-4400 in 1.04 sec, Training loss 0.0000025979\n",
      "    Batches 4401-4600 in 1.06 sec, Training loss 0.0000025968\n",
      "    Batches 4601-4800 in 1.06 sec, Training loss 0.0000025958\n",
      "    Batches 4801-5000 in 1.08 sec, Training loss 0.0000025948\n",
      "    Batches 5001-5200 in 1.16 sec, Training loss 0.0000025940\n",
      "    Batches 5201-5400 in 1.06 sec, Training loss 0.0000025932\n",
      "    Batches 5401-5600 in 1.09 sec, Training loss 0.0000025925\n",
      "    Batches 5601-5800 in 1.10 sec, Training loss 0.0000025919\n",
      "    Batches 5801-6000 in 1.00 sec, Training loss 0.0000025913\n",
      "    Batches 6001-6200 in 1.08 sec, Training loss 0.0000025907\n",
      "    Batches 6201-6400 in 1.05 sec, Training loss 0.0000025902\n",
      "    Batches 6401-6600 in 1.05 sec, Training loss 0.0000025898\n",
      "    Batches 6601-6800 in 1.06 sec, Training loss 0.0000025894\n",
      "    Batches 6801-7000 in 1.04 sec, Training loss 0.0000025890\n",
      "    Batches 7001-7200 in 1.08 sec, Training loss 0.0000025887\n",
      "    Batches 7201-7400 in 1.06 sec, Training loss 0.0000025884\n",
      "    Batches 7401-7600 in 1.09 sec, Training loss 0.0000025881\n",
      "    Batches 7601-7800 in 1.10 sec, Training loss 0.0000025878\n",
      "    Batches 7801-8000 in 1.00 sec, Training loss 0.0000025876\n",
      "    Batches 8001-8200 in 1.05 sec, Training loss 0.0000025874\n",
      "    Batches 8201-8400 in 1.10 sec, Training loss 0.0000025872\n",
      "    Batches 8401-8600 in 1.01 sec, Training loss 0.0000025871\n",
      "    Batches 8601-8800 in 1.10 sec, Training loss 0.0000025869\n",
      "    Batches 8801-9000 in 1.08 sec, Training loss 0.0000025868\n",
      "    Batches 9001-9200 in 1.09 sec, Training loss 0.0000025867\n",
      "    Batches 9201-9400 in 1.08 sec, Training loss 0.0000025866\n",
      "    Batches 9401-9600 in 1.06 sec, Training loss 0.0000025865\n",
      "    Batches 9601-9800 in 1.06 sec, Training loss 0.0000025864\n",
      "    Batches 9801-10000 in 1.06 sec, Training loss 0.0000025864\n",
      "Excluding fixed points with squared speed above tolerance 1e-07:\n",
      "    Kept 796/1257 fixed points with tolerance under 1e-07.\n",
      "Excluding non-unique fixed points:\n",
      "    Kept 796/796 unique fixed points with uniqueness tolerance 0.025.\n",
      "Losses of fixed points:\n",
      "[6.65999265e-13 6.06011330e-09 2.38085285e-08 5.33473568e-08\n",
      " 9.45478433e-08 9.76091741e-08 9.16885483e-08 8.61575415e-08\n",
      " 8.09044991e-08 7.59645360e-08 7.12713586e-08 6.68581208e-08\n",
      " 6.26903471e-08 5.88003104e-08 5.50905099e-08 5.16032301e-08\n",
      " 4.83198406e-08 4.52541258e-08 4.23480842e-08 3.96223072e-08\n",
      " 3.70487712e-08 3.46303040e-08 3.23487406e-08 3.02574215e-08\n",
      " 2.82472659e-08 2.63589506e-08 2.46044749e-08 2.29731363e-08\n",
      " 2.14184297e-08 1.99687626e-08 1.86055527e-08 1.73432770e-08\n",
      " 1.61649201e-08 1.50516115e-08 1.39988554e-08 1.30286271e-08\n",
      " 1.21405392e-08 1.12824772e-08 1.04854365e-08 9.73788694e-09\n",
      " 9.05894026e-09 8.41076098e-09 7.80433673e-09 7.24325000e-09\n",
      " 6.71769840e-09 6.23869001e-09 5.78714587e-09 5.36283240e-09\n",
      " 4.96798558e-09 4.60364724e-09 4.26138635e-09 3.94648136e-09\n",
      " 3.65370711e-09 3.37913297e-09 3.12092130e-09 2.88610558e-09\n",
      " 2.66823008e-09 2.46409915e-09 2.28175923e-09 2.10462936e-09\n",
      " 1.93792205e-09 1.79577042e-09 1.65449099e-09 1.52192681e-09\n",
      " 1.40910150e-09 1.29147426e-09 1.19493970e-09 1.09396570e-09\n",
      " 1.01234499e-09 9.35288291e-10 8.56214044e-10 7.89207921e-10\n",
      " 7.28913485e-10 6.69647671e-10 6.10061723e-10 5.61333868e-10\n",
      " 5.16059973e-10 4.73754591e-10 4.36389869e-10 3.99210220e-10\n",
      " 3.67217146e-10 3.34785144e-10 3.07399106e-10 2.83443435e-10\n",
      " 2.59649496e-10 2.38027875e-10 2.17810200e-10 1.98874819e-10\n",
      " 1.81018270e-10 1.67016345e-10 1.51877580e-10 1.39265835e-10\n",
      " 1.27471325e-10 1.17848092e-10 1.06978613e-10 9.66372538e-11\n",
      " 8.97846728e-11 8.12829318e-11 7.50615126e-11 6.72356892e-11\n",
      " 6.24652205e-11 5.62219646e-11 5.22908453e-11 4.70223305e-11\n",
      " 4.30399986e-11 3.91286899e-11 3.50259058e-11 3.25584594e-11\n",
      " 3.00176099e-11 2.76452854e-11 2.42934301e-11 2.24256152e-11\n",
      " 2.08410719e-11 1.81344766e-11 1.68645965e-11 1.53752931e-11\n",
      " 1.47273513e-11 1.32494779e-11 1.14755011e-11 1.06543047e-11\n",
      " 9.91087247e-12 8.97903626e-12 8.52114386e-12 6.92675344e-12\n",
      " 6.59329882e-12 6.03664341e-12 5.53571902e-12 5.49512172e-12\n",
      " 4.99953551e-12 4.72949978e-12 4.16093332e-12 3.76199072e-12\n",
      " 3.23529007e-12 3.02890091e-12 2.89850218e-12 2.55219110e-12\n",
      " 2.51337579e-12 2.44126854e-12 2.36818638e-12 2.23640442e-12\n",
      " 2.12707434e-12 2.07834292e-12 1.79407606e-12 1.77597260e-12\n",
      " 1.69694900e-12 1.50974827e-12 1.61576915e-12 9.61236407e-13\n",
      " 9.45610127e-13 9.31541302e-13 7.85112481e-13 7.84306105e-13\n",
      " 8.17820367e-13 8.18782650e-13 8.45323811e-13 8.26449748e-13\n",
      " 8.26894163e-13 8.39223276e-13 8.33111249e-13 8.44102457e-13\n",
      " 8.44635288e-13 8.40655562e-13 8.31335055e-13 8.26000618e-13\n",
      " 8.49426866e-13 8.20591208e-13 8.05958327e-13 8.25581682e-13\n",
      " 8.03848795e-13 8.22364095e-13 8.16704831e-13 8.09510445e-13\n",
      " 8.11398149e-13 8.02072493e-13 8.02413041e-13 8.02161126e-13\n",
      " 7.92166137e-13 8.01655834e-13 7.64215731e-13 7.71105890e-13\n",
      " 7.85981415e-13 7.68436150e-13 7.89083100e-13 7.63772184e-13\n",
      " 7.66247634e-13 7.60997114e-13 7.73206802e-13 7.55203083e-13\n",
      " 7.45925240e-13 7.35161986e-13 7.39542867e-13 7.32881529e-13\n",
      " 7.53341888e-13 6.77314921e-13 6.59250866e-13 7.43982458e-13\n",
      " 7.39151850e-13 7.48206401e-13 6.76980499e-13 6.76563406e-13\n",
      " 6.79082983e-13 6.72961144e-13 6.78207002e-13 6.66544402e-13\n",
      " 6.60853750e-13 6.86604744e-13 6.72628077e-13 7.46208000e-13\n",
      " 6.79728301e-13 6.87082715e-13 6.61104309e-13 6.86748726e-13\n",
      " 6.64101966e-13 6.64768100e-13 6.75564205e-13 6.78312766e-13\n",
      " 6.85728655e-13 6.64101911e-13 6.62436577e-13 6.85665934e-13\n",
      " 6.79978155e-13 6.77873502e-13 6.72955940e-13 6.80082184e-13\n",
      " 6.77873881e-13 6.80061367e-13 6.69124586e-13 6.71873147e-13\n",
      " 6.74287882e-13 6.60914899e-13 6.79644709e-13 6.84084788e-13\n",
      " 6.65433854e-13 6.71212218e-13 6.78754795e-13 6.72955615e-13\n",
      " 6.85417055e-13 6.62436252e-13 6.63995822e-13 6.64439912e-13\n",
      " 6.89206559e-13 6.92938870e-13 6.85834202e-13 6.78206731e-13\n",
      " 6.80414980e-13 6.72955615e-13 6.95603406e-13 6.86833403e-13\n",
      " 6.77873502e-13 6.62436252e-13 6.89289771e-13 6.87081143e-13\n",
      " 6.86833403e-13 6.85415754e-13 6.81747193e-13 6.80081859e-13\n",
      " 6.86748293e-13 6.69347336e-13 6.94271030e-13 6.72622494e-13\n",
      " 6.74287828e-13 6.87081414e-13 6.87166415e-13 6.68042011e-13\n",
      " 6.81747139e-13 6.72877498e-13 6.74626099e-13 6.90205651e-13\n",
      " 6.77895240e-13 6.80414872e-13 6.85749146e-13 6.81752398e-13\n",
      " 6.72955615e-13 6.77895240e-13 6.95957994e-13 6.86082213e-13\n",
      " 6.80414872e-13 6.89289717e-13 6.66770892e-13 6.85501081e-13\n",
      " 6.78206189e-13 6.80303849e-13 6.82184290e-13 6.78206189e-13\n",
      " 6.95937123e-13 6.85748767e-13 6.53915236e-13 6.81414072e-13\n",
      " 6.92937840e-13 6.95937123e-13 6.76562972e-13 6.81747139e-13\n",
      " 6.80087009e-13 6.85665825e-13 6.94604855e-13 6.76895985e-13\n",
      " 6.80414817e-13 6.72960711e-13 6.64106736e-13 6.88956650e-13\n",
      " 6.68375078e-13 6.86625127e-13 6.76624501e-13 6.72206106e-13\n",
      " 6.71290172e-13 6.59604316e-13 6.90164018e-13 6.77873393e-13\n",
      " 6.60104675e-13 6.90538664e-13 6.75208533e-13 6.78312333e-13\n",
      " 6.78206189e-13 6.81747085e-13 6.72955506e-13 6.76561997e-13\n",
      " 6.80060934e-13 6.83751666e-13 6.78416470e-13 6.95479210e-13\n",
      " 6.94270162e-13 6.79644654e-13 6.76562972e-13 6.65433745e-13\n",
      " 6.71628443e-13 6.71565993e-13 6.80394001e-13 6.58938128e-13\n",
      " 6.64018211e-13 6.62691148e-13 6.89274050e-13 6.72955506e-13\n",
      " 6.68125223e-13 6.79644654e-13 6.94270108e-13 6.73205307e-13\n",
      " 6.90538664e-13 6.87082281e-13 6.78645399e-13 6.76873921e-13\n",
      " 6.80414872e-13 6.71623293e-13 6.78206189e-13 6.95957940e-13\n",
      " 6.92521073e-13 6.62769210e-13 7.28411147e-13 6.76874247e-13\n",
      " 6.80310734e-13 6.76646239e-13 6.71873039e-13 6.71290172e-13\n",
      " 6.81002943e-13 6.62436197e-13 7.36903485e-13 6.78749483e-13\n",
      " 6.74292978e-13 6.62774414e-13 7.36959864e-13 6.69790558e-13\n",
      " 6.64101478e-13 6.75292179e-13 6.71227722e-13 6.95146089e-13\n",
      " 6.75230650e-13 6.76647052e-13 6.76541126e-13 6.71893856e-13\n",
      " 7.01404700e-13 6.66687625e-13 6.75647797e-13 6.86081834e-13\n",
      " 6.80081750e-13 7.26218456e-13 6.76894684e-13 6.76646998e-13\n",
      " 6.76542156e-13 6.71540026e-13 7.06733771e-13 6.67770472e-13\n",
      " 6.78312333e-13 6.84417800e-13 6.78749537e-13 6.62358081e-13\n",
      " 6.72877498e-13 6.80394055e-13 6.68375023e-13 6.86604311e-13\n",
      " 6.78733870e-13 6.78726931e-13 6.62352877e-13 6.68458290e-13\n",
      " 6.78312333e-13 6.78206569e-13 6.80414817e-13 6.62685998e-13\n",
      " 6.78228307e-13 6.76980119e-13 7.38658158e-13 6.85605110e-13\n",
      " 6.72955561e-13 6.85415700e-13 6.79977667e-13 7.23392266e-13\n",
      " 6.71873039e-13 6.78395599e-13 6.85749092e-13 6.87166361e-13\n",
      " 6.83751612e-13 6.71873039e-13 6.64018211e-13 6.68436606e-13\n",
      " 6.72955561e-13 7.29020956e-13 6.80414817e-13 6.63024215e-13\n",
      " 6.71899060e-13 6.74287774e-13 6.93937963e-13 6.76980119e-13\n",
      " 6.86748347e-13 6.62441347e-13 6.62685943e-13 6.76895985e-13\n",
      " 6.65433745e-13 6.82397661e-13 7.47672811e-13 6.53915182e-13\n",
      " 7.42210438e-13 6.78312333e-13 6.84728695e-13 6.61436997e-13\n",
      " 6.72955561e-13 6.67770093e-13 6.82087091e-13 6.76873921e-13\n",
      " 7.67185415e-13 7.24358832e-13 6.68103539e-13 6.69458304e-13\n",
      " 6.66709689e-13 6.61658987e-13 6.62691148e-13 6.59166244e-13\n",
      " 7.33351476e-13 6.78561320e-13 6.74287774e-13 7.17369632e-13\n",
      " 7.51203570e-13 6.55247449e-13 6.67126077e-13 6.68459103e-13\n",
      " 6.76874247e-13 6.79165816e-13 7.19085273e-13 6.68125277e-13\n",
      " 7.48894544e-13 6.85749092e-13 6.74620841e-13 6.72955506e-13\n",
      " 6.86997768e-13 6.77646253e-13 6.68352960e-13 6.78499737e-13\n",
      " 6.76411130e-13 6.78206460e-13 7.42233315e-13 6.68375023e-13\n",
      " 7.47451363e-13 6.64018211e-13 6.78206514e-13 6.69458304e-13\n",
      " 6.77895240e-13 6.72872294e-13 6.53920440e-13 6.71566047e-13\n",
      " 7.14089269e-13 6.87082335e-13 6.69874638e-13 6.62358081e-13\n",
      " 6.62774414e-13 6.64434545e-13 6.68042011e-13 6.85521843e-13\n",
      " 6.69352486e-13 6.79082550e-13 6.90538664e-13 7.35016160e-13\n",
      " 6.69458304e-13 7.42127171e-13 7.50782032e-13 6.72622494e-13\n",
      " 6.85748767e-13 6.87499428e-13 6.87081034e-13 6.81747085e-13\n",
      " 6.63435344e-13 6.94270054e-13 7.35433361e-13 6.76562972e-13\n",
      " 6.80414817e-13 6.74287774e-13 6.81086155e-13 6.76980065e-13\n",
      " 6.76562972e-13 6.72955561e-13 6.62691202e-13 6.64106682e-13\n",
      " 6.64018211e-13 6.87082281e-13 6.79644654e-13 6.86748347e-13\n",
      " 6.81752289e-13 6.83079353e-13 6.75563772e-13 6.78645454e-13\n",
      " 6.92604828e-13 6.64101532e-13 6.80414872e-13 6.87081034e-13\n",
      " 6.79977721e-13 6.78206189e-13 6.70540826e-13 6.81414072e-13\n",
      " 6.76873921e-13 6.86750136e-13 7.58670579e-13 6.70207759e-13\n",
      " 6.72955561e-13 6.69435861e-13 6.70124492e-13 6.78561374e-13\n",
      " 6.80414872e-13 7.49371593e-13 6.76874301e-13 6.70540826e-13\n",
      " 6.78228307e-13 6.71290226e-13 6.72960765e-13 6.55252708e-13\n",
      " 6.80414872e-13 6.84084733e-13 6.78645508e-13 6.76874409e-13\n",
      " 6.74287882e-13 7.09759508e-13 6.78228361e-13 6.79644709e-13\n",
      " 6.85749200e-13 6.81747193e-13 6.72955615e-13 6.94519637e-13\n",
      " 6.87166524e-13 6.78206298e-13 6.77750445e-13 6.85542823e-13\n",
      " 6.78206623e-13 6.79977830e-13 6.70456854e-13 6.62658296e-13\n",
      " 6.65766921e-13 6.85749255e-13 6.80081859e-13 6.78228361e-13\n",
      " 6.62769319e-13 6.72877552e-13 6.72544485e-13 6.72955615e-13\n",
      " 6.84084788e-13 6.61437051e-13 6.78206623e-13 6.70296609e-13\n",
      " 6.81747519e-13 6.77895619e-13 6.78645833e-13 6.76874735e-13\n",
      " 6.72955994e-13 6.80082238e-13 6.77873556e-13 6.78312766e-13\n",
      " 7.43987337e-13 7.60108176e-13 6.80415251e-13 6.91522360e-13\n",
      " 6.78312820e-13 7.54756392e-13 6.71290606e-13 6.81747519e-13\n",
      " 6.85749580e-13 7.29577314e-13 7.10258675e-13 6.56913217e-13\n",
      " 7.47540268e-13 7.54339733e-13 7.44398792e-13 7.53584261e-13\n",
      " 6.81747519e-13 7.40518215e-13 6.72961144e-13 6.68875870e-13\n",
      " 6.75231084e-13 7.58775963e-13 7.62333230e-13 7.62329002e-13\n",
      " 7.47563957e-13 7.64241860e-13 7.68880239e-13 7.58670850e-13\n",
      " 7.66436610e-13 7.76870322e-13 7.97190439e-13 7.77563669e-13\n",
      " 8.07823318e-13 7.70543948e-13 7.81200246e-13 7.93420397e-13\n",
      " 8.03848795e-13 8.04319881e-13 7.78006023e-13 8.04292451e-13\n",
      " 8.09515541e-13 8.07931196e-13 8.13174398e-13 8.05957731e-13\n",
      " 8.13152388e-13 8.18372497e-13 8.02072438e-13 8.11396306e-13\n",
      " 8.20587738e-13 8.31334892e-13 8.38773061e-13 8.29996445e-13\n",
      " 8.34909941e-13 8.40988629e-13 8.39217476e-13 8.38768779e-13\n",
      " 8.39322318e-13 8.45987397e-13 8.37552033e-13 8.33891495e-13\n",
      " 8.40993507e-13 8.34414027e-13 8.28647264e-13 8.13457483e-13\n",
      " 8.06407946e-13 7.95583001e-13 9.41124132e-13 9.79323827e-13\n",
      " 1.04366017e-12 1.01703628e-12 1.55415351e-12 1.55973064e-12\n",
      " 1.75677268e-12 1.97825675e-12 2.10312323e-12 2.08514369e-12\n",
      " 2.22232389e-12 2.38751120e-12 2.47662741e-12 2.52247355e-12\n",
      " 2.54453078e-12 2.65023550e-12 2.83581665e-12 2.90924641e-12\n",
      " 3.10262102e-12 4.07886658e-12 4.07832362e-12 4.95156520e-12\n",
      " 5.22558212e-12 5.52420349e-12 5.55981303e-12 5.85516271e-12\n",
      " 6.68958205e-12 6.90074517e-12 8.48250983e-12 9.09801921e-12\n",
      " 9.81412868e-12 1.01604645e-11 1.13349807e-11 1.33576761e-11\n",
      " 1.39126011e-11 1.52543360e-11 1.61737915e-11 1.76799790e-11\n",
      " 2.04291237e-11 2.17683579e-11 2.36094096e-11 2.59116773e-11\n",
      " 2.88016989e-11 3.12964966e-11 3.37667741e-11 3.76206635e-11\n",
      " 4.08933720e-11 4.50029319e-11 5.01595189e-11 5.36318490e-11\n",
      " 6.04010175e-11 6.47649157e-11 7.07944259e-11 7.83746332e-11\n",
      " 8.46290538e-11 9.34271965e-11 1.02205598e-10 1.11236756e-10\n",
      " 1.20586402e-10 1.32406017e-10 1.45912754e-10 1.57893060e-10\n",
      " 1.73145345e-10 1.90823704e-10 2.07872386e-10 2.26513391e-10\n",
      " 2.46359877e-10 2.69641032e-10 2.95570513e-10 3.20299870e-10\n",
      " 3.51708329e-10 3.82457233e-10 4.14832335e-10 4.53349358e-10\n",
      " 4.92907659e-10 5.39130851e-10 5.84944204e-10 6.35859587e-10\n",
      " 6.94486135e-10 7.50536078e-10 8.18828783e-10 8.88272678e-10\n",
      " 9.66443037e-10 1.04974163e-09 1.14148735e-09 1.23731025e-09\n",
      " 1.33976252e-09 1.45741863e-09 1.57475388e-09 1.71376779e-09\n",
      " 1.85829607e-09 2.00666173e-09 2.17927409e-09 2.35506326e-09\n",
      " 2.55003352e-09 2.75939627e-09 2.98689229e-09 3.22779359e-09\n",
      " 3.49273721e-09 3.77717413e-09 4.06882350e-09 4.41011672e-09\n",
      " 4.74947770e-09 5.12270759e-09 5.53060442e-09 5.96623018e-09\n",
      " 6.42973896e-09 6.93385704e-09 7.47874296e-09 8.05466449e-09\n",
      " 8.67119088e-09 9.32358901e-09 1.00421147e-08 1.08030491e-08\n",
      " 1.16187726e-08 1.24903092e-08 1.34355682e-08 1.44321213e-08\n",
      " 1.54916400e-08 1.66318657e-08 1.78525674e-08 1.91507539e-08\n",
      " 2.05502513e-08 2.20345182e-08 2.36279476e-08 2.53021000e-08\n",
      " 2.71166076e-08 2.90485005e-08 3.10840207e-08 3.32737500e-08\n",
      " 3.55938887e-08 3.80514464e-08 4.06955749e-08 4.34892549e-08\n",
      " 4.64846650e-08 4.96325185e-08 5.29930091e-08 5.65101779e-08\n",
      " 6.03326100e-08 6.43396731e-08 6.86328434e-08 7.31181160e-08\n",
      " 7.79278864e-08 8.29958395e-08 8.83774334e-08 9.40493692e-08\n",
      " 7.70019071e-08 4.03541378e-08 1.54598254e-08 2.29774755e-09]\n"
     ]
    }
   ],
   "source": [
    "candidates = model.get_stimulus_by_pos(bm.arange(-bm.pi, bm.pi, 0.005).reshape((-1, 1)))\n",
    "\n",
    "finder = bp.analysis.SlowPointFinder(f_cell=model, target_vars={'u': model.u})\n",
    "finder.find_fps_with_gd_method(\n",
    "  candidates={'u': candidates},\n",
    "  tolerance=1e-6,\n",
    "  num_batch=200,\n",
    "  optimizer=bp.optim.Adam(lr=bp.optim.ExponentialDecay(0.1, 2, 0.999)),\n",
    ")\n",
    "finder.filter_loss(1e-7)\n",
    "finder.keep_unique()\n",
    "# finder.exclude_outliers(tolerance=1e1)\n",
    "\n",
    "print('Losses of fixed points:')\n",
    "print(finder.losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa43d9dd",
   "metadata": {},
   "source": [
    "## Visualize fixed points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53958d6c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:59.148606100Z",
     "start_time": "2023-07-22T05:49:58.976578900Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmM1mxMbGora2lvVHREREfsLV63dA1xwRERERtRXDEREREZECwxERERGRgl8VZBMRuUNhUTm2V1Tj6Ok6wACkxZnk/+8WH4UWIXC0pg5CCKTHR8n/f2f/dMzIzfJ184nIwxiOiCjohIYYUHrotPz90Zo6zf8HgGNn6q1+jogCH4fViCjoTB/RCzPb2AM0MzcL00f08lCLiEhPGI6IKCi1JSAxGBEFF4YjIgpa00f0QkSo47fBiNAQBiOiIMNwRERB66XN+9FoaXF4TKOlBS9t3u+lFhGRHjAcEVFQemnzfiwpKnfp2CVF5QxIREGE4YiIgk5bgpGEAYkoeHAqPxEFHUuLwKAe8W1e58jSwq0oiYIBwxERBR0u5EhEjnBYjRwqdDCU8NLm/Shs49AEERF5H9/L24Y9R2RXYVE5Pth5VF4xWDmdefLfSlF8sBqDesT7qnlEROSi7RXVKD10GqWHqvHOQ4Pk26X6u7Q4EwD2qkoYjshGYVE5Pig7CoPh4lYKyuLV5V/sR6OltfYip2eiT9pIRESuy+mZiNJDp1F8sBqXP/Upfjv8MgAX39uP1tRh/c6jeL+sknsIAjAIIVhh2EZmsxmxsbGora1FTEyMr5vjVureovQ4EypVe01JuGowEZH/cDRLU/lenxZnwvjr0gIyILl6/WY4aodADEfK3iJ1GIqJDIO5vtnqNgYjIiL/oxWQtN7j0+NMaBEi4HqRXL1+c1iNLvYWndHuLVL/0RARUeDQCkbSNeCDnUcBBF8tEmerBTn1MBrQ2nOU/nNxnj1cEI+IyL+4svip+sPx0Zo6fLDzaNDNZmM4CmITXy3BelUwktirM1KGJgYkIiL/oA5G9j4Aa733S8XaE18t8Vj79IbhKEhNfLUE+06YXeolUlIfX3zwlCeaR0REbqR8r3Y00UaLdPy+E+agCUisOQoyUuG1ub4J5vpmxESGyYHH3h+LulhPOr5rnAnZmQneajoREbWT9F59rKbOpUk3EunaIB2z74QZQxZtDrhCbTWGoyCiLryWXuxSQLLHXN9sFZ5iIsOQ2smEtQ8P9kq7iYjo0khBZuKrJaita5LDkLNeJGUwkv5rrm8O+EJtTuVvB3+cyq9VeA04/sSgpuwtCtQ/CCKiQFdYVI7tFdWavUj2aF0r/HE9JE7lJyvbK6o1C6+1gpHWJwn2FhERBQZ7vUgSrWuA1rXiaE0dtldUe66hPsSC7CAw8dUSHGvDpwN10XVanAn3DcnEukcYjIiIAsW6RwbjviGZ8r5qgHWNkSuO1dQFZJE2e44CnDQrTV03pEVdg8RhNCKiwCa9tyuH2dQ1RvZI15TauiZMfLUkoD5As+aoHfyl5kgZjKQXeVsC0pUpMQH1YiciIvu0rhn2qGex+cs1w9XrN4fVApTWi9zZrDQAfvUiJyIi91n3yGBcmRLj0kQdrR6mQFoHieEoANkLRq7MSmMwIiIKXsqA5IzWNSZQAhLDUYApLCrH8TN1LgUj9crYLLwmIiKtQm1Ae8sRrWvN8TN1fr8XG8NRAJHWMpKKqR0FI/WsNH9cr4KIiDxjRm4Wxl+XJgckR7PYtOpa/X2zWs5WCxDqRR4dbQmiNSttHIMREREpSNeE9T9/6HY0GqGe8HP054CkfBx/wp6jAKG1yKOzYCT9N7WTyS9fvERE5FkzcrOQ2smkee1QU19z/HmRSIajAFBYVK65+rWa1oubxddEROSIehabo4CkdrTGP+uPGI4CgL2tQZQYjIiIqL3aG5CO+mn9EcORn3N1axBpPJjBiIiI2kMdkKRrijP+OLzGcOTHpPWM1Huh2SMdx2BERETtIQUkZ7stqPnbHmwMR37smGI9o8qaOhjDnP9zdo0zMRgREVG7rXtkMLq68IFcIgWpY2dcD1O+xnDkpya+WgLDz/9vrm+GMSwEDc0tDn8m7edNZImIiC5FdmaCzSKRWpTbVhkAv+k9YjjyQ9Iq2MrhNFeCERd5JCIid1AvEmmPVJMk9R75y+rZDEd+6P2ySqtFHrVmC2htDcJgRERE7jIjN8ul3iNjWIjVNeuDsqNeaN2lYTjyM4VF5QgxtA6oKbcJUQoNMdhsDcLhNCIicjet4TV1/WtDc4v18JoBuu89YjjyM9srqq2Cj9ZsAUuLsNoahMNpRETkCVp7sGmVeaiH1/Q+tZ/hyI8oV8K2NzstIrS1V4lbgxARkTdIAUk5vV/r+iQNrwH6Xzmb4ciPqFfC1krnjRYh9yrFRIZz2j4REXncjNwstAgBwH7vkfI2vS8MyXDkJ1zdP01K7ulxJozvn+aFlhEREQF39k+3ugY5o+eFIZ3vGke64Mr+acDFIm0OpxERkTfNyM1C6aHW3iBnq2dLIUp4o2HtwJ6jACIldQFwOI2IiLxu3SOD5cBjr/fIgIvhqVt8lC5rjxiO/ICrm8tKvUZdO7m+rDsREZE7de1kcrj3mhSecnomoPhgtS7XPWI48gPHVKthO8K904iIyJdc2XstItSA4oM/F2QbHB7qEwxHOldYVI5u8VEAnI/hEhER+YNGy8VqIz0OrflVONq2bRvGjh2L1NRUGAwGfPjhh1b3CyEwb948pKamwmQyYdiwYdi7d6/VMQ0NDfjd736HxMREREdH49Zbb8XRo/rr0pO8X1aJ4oPVyOnpfIVrroRNRER6oFw529Goh16H1vwqHJ0/fx59+/bF8uXLNe9/4YUXsGTJEixfvhw7duxAcnIycnNzcfbsWfmYgoICbNiwAWvXrsXXX3+Nc+fOYcyYMbBYLN56Gi5TbhUidz86wP3TiIhID7QWhtQiXdv0tqWIX4Wj0aNH47nnnsO4ceNs7hNCYOnSpXjyyScxbtw49O7dG2+++SYuXLiAd955BwBQW1uLlStX4sUXX8TIkSPRr18/vP3229i9ezc+//xzbz8dp9Rbhagph2nZa0RERHqiXBjS0eiHHrcU8atw5EhFRQWqqqowatQo+Taj0YihQ4eiuLgYAFBWVoampiarY1JTU9G7d2/5GC0NDQ0wm81WX95UWVMHg0bBmgCsNpdlrxEREenJnf3T5aEze/RYTxsw4aiqqgoAkJSUZHV7UlKSfF9VVRUiIiIQFxdn9xgtCxcuRGxsrPyVnp7u5tbbUk/fF3ZWypJ6lthrREREejMjNwtHTl9w6Vg9rZgdMOFIYlB1sQghbG5Tc3bME088gdraWvmrsrLSLW11xJXp+1I3pRBgrxEREemSaMPQ2rEz+uhFCphwlJycDAA2PUAnT56Ue5OSk5PR2NiImpoau8doMRqNiImJsfryNKnK31khW07PBO6hRkREutWWobU0F9bz84aACUeZmZlITk5GUVGRfFtjYyO+/PJL5OTkAAD69++P8PBwq2NOnDiBPXv2yMfogXKWmj0xka3b4h05fYG9RkREpFvKoTXp2mVPiMGgi1lrfrXx7Llz53DgwAH5+4qKCnz33XeIj49Ht27dUFBQgD/96U/o1asXevXqhT/96U+IiorC5MmTAQCxsbF44IEHMGvWLCQkJCA+Ph6zZ89Gnz59MHLkSF89LRvvl1Xi2Jl6h1MgzfXN8gazREREeta1k8lqTzUt6XEmFB+sxpFq33/o96tw9O2332L48OHy9zNnzgQA5OXlYfXq1ZgzZw7q6uowdepU1NTUIDs7G5s2bULHjh3lnyksLERYWBgmTJiAuro6jBgxAqtXr0ZoaKjXn489Uv2Tswr+rnEmrH2YW4UQEZG+rXtkMCa9VuLwuibfp4PtRAxC2JsHRfaYzWbExsaitrbW7fVHhUXl2HH4tMOx2ZjIMJjrmzGoRzzDERER+YVJr5Wg9NBp+RpmT07PBFzfPd4jvUeuXr/9qucoGGyvqHb64pGG1Dh9n4iI/EV2ZgKO1dQ57D2KiQxD8cFqefFIXwmYguxA4yhVA5y+T0RE/kW5YrY9zq593sJwpDOVThbLightHYxNi2chNhER+Zf0+CgAgDHMcfw4etq36x0xHOmIK1P4Gy0COT0TOKRGRER+JzszATk9E9DQ3OLwOF9vRMtwpCPSRrOhIY4DEtc2IiIif+TKdiKhBvh8I1qGIx2ytGiPycqLZ3F+IRER+Slpkry9BSEtOrjGMRz5EXN9M7cLISIivyZtJ6KX4mstDEd+pkUIDqkREZHfcmXWmq8xHOmEK8XYREREwcKX+6xxEUidkBZ/DA0xaNYchRpax2GPOtlShIiISO+ka5mja54vF4NkONIJaX0je8XYFgFuNEtERAHB2Ua0UlG2r9Y74rCaThhcGFLrGmfCuke4lxoREfm3dY8MRtc4Fz7s+6jahOFIJ9JceZEQEREFEV9dGxmOiIiISJd8VZTNmiMd4Ew1IiIKVsawEM3tRCJCDT4rymY40gFpppojOT0TcH33eC+1iIiIyLOyMxMQYmgNQFoafbhUNofV/AQXfyQiokCi58UgGY78BNc3IiKiQKPXaxvDkb/QZ7gmIiJqN8GeI7oUafGc6k9ERIElPT7K103QxHBEREREPpGdmYCYSMdzw3wx9MZwpAPO/uFjIsOQnZngpdYQERF5x4zcLKdVI7V1TV5pixLDkQ44+4cXAGeqEREReQnDkY8VFpU73Tom1hTulbYQERF5m7NrnAHw+irZDEc+tr2iGub6ZofHcN81IiIKVM6uceb6Zmyv0F4o0lMYjoiIiIgUGI6IiIiIFBiOiIiIiBQYjoiIiIgUGI6IiIiIFBiOfIwLQBIRUTDT4yrZDEc+xgUgiYgomOlxlWyGIyIiIiIFhiMiIiIiBYYjIiIiIgWGIyIiIiIFhiMiIiIiBYYjIiIiIgWGIyIiIiIFhiMiIiIiBYYjIiIiIgWGIyIiIiIFhiMiIiIiBYYjIiIiIgWGIyIiIiIFhiMiIiIiBYYjH4s1hTu83wCgsKjcO40hIiIihiNfS4szObzfXN+M7RXVXmoNERGRdxUWlcPg5BhnHQnuxnBEREREPrO9ohrm+maHxzjrSHA3hiM/kNMz0ddNICIi8gg9XuMYjnQuJjIMlhbh62YQERF5hKVFICYyzNfNsMJwpCNaLw7WHBERUSBzZVjN2xiOdERvLw4iIqJgFFDhaN68eTAYDFZfycnJ8v1CCMybNw+pqakwmUwYNmwY9u7d68MWA9mZCU67E4/W1HmpNURERBRQ4QgArr76apw4cUL+2r17t3zfCy+8gCVLlmD58uXYsWMHkpOTkZubi7Nnz/qsvTNys+Csoqi2rskrbSEiIvI2Zx0AMZFhyM5M8FJrWgVcOAoLC0NycrL81blzZwCtvUZLly7Fk08+iXHjxqF379548803ceHCBbzzzjs+bjUREVFwctYBINDakeBNAReO9u/fj9TUVGRmZmLSpEk4dOgQAKCiogJVVVUYNWqUfKzRaMTQoUNRXFzsq+YC0C7Ebsv9RERE/kqP18CACkfZ2dl466238O9//xt/+9vfUFVVhZycHFRXV6OqqgoAkJSUZPUzSUlJ8n32NDQ0wGw2W325U0ZCtMP7QwwGbiFCREQBp7CoHCEGx+tjO7tGekJAdUmMHj1a/v8+ffpg8ODB6NmzJ958800MGjQIAGBQ/SMIIWxuU1u4cCGeeeYZ9zf4Zy3CcdVRZU0dp/MTEVHA2V5RjUonNUfOrpGeEFA9R2rR0dHo06cP9u/fL89aU/cSnTx50qY3Se2JJ55AbW2t/FVZWemxNhMREZFvBXQ4amhowL59+5CSkoLMzEwkJyejqKhIvr+xsRFffvklcnJyHD6O0WhETEyM1Ze36XF5dSIiokuh12tbQIWj2bNn48svv0RFRQW2b9+OO++8E2azGXl5eTAYDCgoKMCf/vQnbNiwAXv27EF+fj6ioqIwefJkXzfdIW4hQkREgUiPW4cAAVZzdPToUfz617/GqVOn0LlzZwwaNAilpaXIyMgAAMyZMwd1dXWYOnUqampqkJ2djU2bNqFjx44+bvlFMZFhNitlcwsRIiIKRPa2DtG6FnpTQIWjtWvXOrzfYDBg3rx5mDdvnnca1A7cQoSIiIKdr6+FATWs5q+yMxOQHmdyeMyxmjpO5yciooBRWFSOY05mqqXHmby+OjbAcKQLM3Kz0NVJOOJ0fiIiCiSuTOPvGmfy+urYAMOR7umxUI2IiMid9HatYzjSiezMBM0Xh6/HXYmIiDzNXlG2L4bUAIYj3QgNMTAIERER/cxc34zQEMc7WHgKw5FOFB885fQYvS6WRURE1FauXNNcuTZ6AsORztgbd5Vu54w1IiLyd9K1zNk1z1f0VQEVxLIzExBiMKD4oPaMNHN9M5YUlWNQj3gvt4yIiMi9tldUo/TQabv3m+ubkdMzAdd39801jz1HOjEjN8snOw8TERHpUYsQPpnGDzAcEREREVlhOPIzIQYD646IiIg8iDVHOmRvw72YyDAUH6zm8BsREfmtwqJyhBh8M0XfVQxHOpKdmYCcnokoPVStWZgtBSZO6SciIn8VGtI6+cheR0B6nAl3DUiHpcV3HQEcVtMRqfDM3ow1oPVF48sXDBER0aWwtAikx5nsLnws7bfmq2JsgOFId5wteMUNaImIyJ+5suGsrxZ/lDAc+SEWZRMRkT/yh3ojgDVHuhURakCjxXb4zBgWwqJsIiLyS9Lij/bqjfSCPUc601qUnaAZjACgobnFyy0iIiJyL3vByNfbhkgYjnSGK2UTEVGwkrYNyc5M8Gk7GI50KDszAelxJofHcDo/ERH5G2fXrvQ4E67vHu/TmWoAw5EuhYYYHFby5/RsTdQsyiYiIn8hXbOka5iWypo6hIb4vmBbH4N7ZEWawmivYG3PsVoUH6zGoB6+2a2YiIiorZTF2Fqka17xwVOYPqKXl1tnjeFIh7IzExBiMNhdDFLPFf5ERESO2LuGSfVG13f3/Qd/DqvpkKtF2VzviIiI/IGr6xu1COHzeiOAPUd+i5vQEhGRv/CX9Y0k7DnSuTQ7s9b84cVFRESkZO/aZe9a5yvsOdKp1sUgE1F6qBpHHc5c45R+IiLSt9br2Wm793eLj8KEAem62VidPUc6JY252ivKBjiln4iI9M+VKfzStU4P9UYAe450zdmuxEdOX+CUfiIi0jWp3sjZ0JkepvBL2HPkB+ytCeFouI2IiEhP7F2z9LKfmhLDkY5Jm9A6K77mlH4iItIjV6bw62U/NSWGIx1zZb0jaUr/9gr7tUlERES+sL2iGsUHq532DullfSMJw5GfsFfIJvUqcdYaERHpjXRtsjcC4qhI25cYjnQuOzMBM530IOX0TNDN9EciIiKJpUU4DEAtQmBmbpauhtSANoSjpqYmzJkzB5dddhkGDhyIVatWWd3/448/IjQ01O0NDHZSN6Oj9SGKD1Zjx+HTrDsiIiLdKCwqx47Dpx0uSSNd2/Q0pAa0IRwtWLAAb731FqZMmYJRo0ZhxowZeOSRR6yOEdzKwiOcTeln3REREemNq/VGzq5xvuByOFqzZg1ef/11zJ49G8899xzKysqwZcsW3HfffXIoMriwqRy1X7qTrUQ4a42IiPRAOUvNXr2RvWuaHrgcjo4dO4bevXvL3/fs2RNbt25FSUkJ7rnnHlgsFo80kC5O6a90sK5RepyJvUdERKQLUq+RowBUWVOnuyn8EpfDUXJyMg4ePGh1W2pqKr744gvs2LEDeXl5bm8ctVJO6bf3QpOCE2etERGRr0nXInsf6qVrmd6m8EtcDkc33ngj3nnnHZvbpYB0+PBhd7aLVJS9R/bGbzlrjYiI9MDRLLWYyDBd9xoBbQhHf/zjHzFhwgTN+7p27Ypt27bhjTfecFvDyFpoiEHuotQav5WKsjlrjYiIfEk5S03rw7y5vlkuBQkN0WetsssbmmRkZCAjI8Pu/SkpKRxa8yAphdubEql8sTlbVZuIiMhTpI1m0+NMdofVpJ4jvY52cBFIP9GWuiPOWiMiIl9QzlLz13ojoA09R+R72ZkJCDEYHC6oxd4jIiLylbb0Gl3fPd7LrXMde478CGetERGRnvn7LDUJw5GfcWXW2syfX3AcWiMiIm+Rrjkz7YQef5ilJnE5HNXU1GDZsmUwm80299XW1tq9j9xLmrWW0zNBc9aalMqXFJVzQUgiIvKa7RXVWPJzQNIa3TDXN8sTi/Q6S03icjhavnw5tm3bhpiYGJv7YmNj8dVXX2HZsmVubRzZcjZrrbKmTn5xsjCbiIi8bUlRud1hNenDvV5nqUlcDkcffPABpkyZYvf+Rx55BO+//75bGkX2KeuO7C2wJd3H7USIiMgblLPU7PGXeiOgDbPVDh48iF69etm9v1evXjbbi5BnuDJrzdF9RERE7hQos9QkLvcchYaG4vjx43bvP378OEJCWN/tDa72HrXez1lrRETkWc5mqUnXKn/oNQLaEI769euHDz/80O79GzZsQL9+/dzRJnJBdmYCZuZmYVAP++GIs9aIiMjTnM1SA4BBPVqvWXqfpSZxORxNmzYNL774IpYvXw6LxSLfbrFYsGzZMhQWFuK3v/2tRxpJtqTkvcRB8Ck9VM1Za0RE5FHSLLXSQ/avNdK1yh96jYA2hKPx48djzpw5mD59OuLj49GvXz9cd911iI+PR0FBAWbOnIk777zTk20lleKDpwDYXxBSqjvirDUiIvIEZSG2s1pX6ZrlD9pUJLRgwQKUlpYiPz8fqampSE5Oxn333YeSkhIsWrTIU230iBUrViAzMxORkZHo378/vvrqK183qc2UC0LaI20nwt4jIiJyt+0V1fL0fHuc1cbqUZv3Vhs4cCAGDhzoibZ4zbp161BQUIAVK1ZgyJAhePXVVzF69Gh8//336Natm6+b57IZuVmY9FqJw2PUm9H6S5cmERHpm6u9RlJ48odZahKXe44uXLiA3/72t+jatSu6dOmCyZMn49Qp/+kiU1qyZAkeeOABPPjgg7jyyiuxdOlSpKen4+WXX/Z109ptZm6W3eE1f1mRlIiI/IdyxwYt6XEmuUjbX2apSVzuOZo7dy5Wr16Nu+++G5GRkXj33Xfx6KOP4h//+Icn2+d2jY2NKCsrw+OPP251+6hRo1BcXKz5Mw0NDWhoaJC/19M2Ka1Da/anUMZEhvnNiqREROQ/lDs2xESG2WxpJV2TZuZm+d31x+Weo/Xr12PlypV47bXX8NJLL2Hjxo348MMPrWau+YNTp07BYrEgKSnJ6vakpCRUVVVp/szChQsRGxsrf6Wnp3ujqS5xNmvNXN8s1x3tOHyahdlERHTJCovKsePwaRQfrEZ6nElzr0/A/2apSVwOR5WVlbjhhhvk7wcOHIiwsDCHC0PqmUG1zLkQwuY2yRNPPIHa2lr5q7Ky0htNdJk0A8Be16a0KikLs4mIyB2UhdjOFn70p1lqEpeH1SwWCyIiIqx/OCwMzc3aaVGvEhMTERoaatNLdPLkSZveJInRaITRaPRG89qlLduJsDCbiIguRSAXYktcDkdCCOTn51uFhPr6ekyZMgXR0dHybevXr3dvC90sIiIC/fv3R1FREe644w759qKiItx2220+bFn7KWetST1EWpT3MSAREVF7SPuouXK98bdCbInL4SgvL8/mtt/85jdubYy3zJw5E/fccw8GDBiAwYMH47XXXsORI0cwZcoUXzet3ZS9R/ZesMr7HG07QkREZE9Oz0SUHjptNxhJda7+2msEtCEcrVq1ypPt8KqJEyeiuroa8+fPx4kTJ9C7d2988sknyMjI8HXT2m1GbpZcbF18sBppcSYcVY0DpylesP42c4CIiHyvsKgcoSEGzMzN0pwIFBMZJte5Xt893i97jYA2rpAdSKZOnYrDhw+joaEBZWVl+OUvf+nrJl0y5ZoT6mAEAEcVhdmcuUZERG0hzVCTQpHW2nrm+uaAWFuvzStkk34p15wAgIhQAxot1j1EyqG1FsHeIyIico2y1kir18gYFoKG5paAGKEI2p6jQDQjN0sOPDk9E2yCEXCxdwnghrREROQa9Qy1iFDbXqGG5hZ5+r6/FmJLGI4CjLQZrb0l3aUkHwjdnkRE5B3qDWbVH75jIlsHoqRjsjP9e9IPw1GAmZGbheu7x8vhJ83OfmuB0O1JRETeIW1TJW0Vota7a6zf7qOmheEoACkDklZhNnBx5hoLs4mIyBHpGiGFH/VWIdIentIx/t5rBDAcBSxnuyVz5hoREblie0W1SzPU/HUfNS2crRag1DPXQg2Auj6bM9eIiMgRZSG2vQ3OgcAr1WDPUYBSz1zTmLgGY1gIZ64REZEmaV0jR6MQAAJmhpoSw1EAczZzraG5BQBnrhERkS1leYbWViGBNkNNieEogLkyc41bihARkRZleYbWDLWrUmMCaoaaEsNRgOOWIkRE1FbqITX1DDUAKD10GkDgzFBTYjgKcMrkb2/MWNltyoBERETKRR+1htSMYa3xIZBmqCkxHAU49dAa0DpzTU35R7C9wvYPgYiIgoN6qxCta4Zyq5Dig6e82TyvYDgKApy5RkRErtCaoaZ1zVCOSATakBrAcBQ0OHONiIiccTZDDbAORtd3jw+4ITWA4ShocOYaERE5o6xTdXadCNRgBDAcBRXOXCMiInvUQ2rOrhOBPMLAcBREOHONiIi0qIORK4s+BvIIA8NREOHMNSIi0qKeuq++NoSGGOQNZoHAW/RRjeEoyHDmGhERKamn7sdEhtlcG9QjD4E4Q02J4SgIceYaEREB2lP3tVbDDoYZakoMR0FIPbymFZCkGQnSvjnsPSIiCjzqqftaM9SCLRgBDEdBS/0Hod5U8GhNnRyMlhSVs/aIiCgAqYfL1DPUlFP3g2kkgeEoSKn/ILS6Uf/xbaW8bw5rj4iIAosrM9SUU/cDfYaaEsNRkNKauabuPar8+RMEp/YTEQWW9kzdD5YhNYDhKKipZ66Z65ttApI0c40BiYgocHDqvmNhzg+hQJadmYAQg8Gq+HqJIvw0NLcgXTXmLAUqIiLyP1pT99WlFerSi+u7x/uiqT7DnqMgJw2vaQUjSaVizBkAcnomerWNRETkPsoJOQCn7mthOCL5RS8FI62p/VIw4tR+IiL/Jb13z8zN4tR9BxiOCABQfPAUgIt/FOkafzDK3iXWHhER+RepCHuJIiCpp+6ryyiCZeq+GmuOCIB17ZH0RxERakCjYg351786JBfosfaIiMi/bK+oRumh08jpmYAlReWaH4Irg3Tqvhp7jgiA9qrZjarNdaTZbNx3jYjIv6iLsNPjTPJyLRIpLAX7kBrAcEQKWmsfqT9ZSIV7nNpPROQftPZP0wpGUq8REHxT99UYjsiKcu2jmblZuGtAus0xUu8RAxIRkb5pLfaoNZx214B0uUg7p2cCsjNtJ+YEE4YjspGdmWBVfK2evaasOwr2oj0iIj1T76OZ0zPBptdIqkECWj8UB/NwmoThiGzMUAUjrWXl1X9swVq0R0SkZ+rFHB29n0sBKdiDEcBwRHYo/6AA29ojABxaIyLSMVf2T1MXYfODbiuGI9Kk3netsqbOZt81gAGJiEiPXN1YlkXY2hiOyK7szASr7lhzfTOMYdYvGW5MS0SkL1rBSOu9W10/GuxF2EoMR2SX1tpHDc0tVsc0NLfYzF7bXmH7CYWIiLxje0W11XtyTGSY5ns3twmxj+GIHNIKSGrm+mZ5yXmAi0MSEfmK1mKP3Fi27RiOyClXApI0NZRT+4mIfEc5dR+wXewRYDByBcMRuURrrQw16T5pjST2HhEReU+hYq0iZ+/T/CDrGMMRuURrrQz19H5lMFryc0EgAxIRkedJRdhLVAFJSSp/4Bp1ztnOzSbSMCM3Sw46jqaG/uPbSqtdnYHWP1p22xIRec72imqUHjotL+aotTad8r2ZQ2qOseeIXKa1Ma2627ayps7m0wlnrxEReY5WEbbWxrLS/QxGzjEcUZuoF4fUGtdW9xxx9hoRkWeo1zQCbIuwpbDExR5dx2E1arPszASEGAxWNUbqITZlzxKH14iI3E9rsUetXqO7BqQDuLhf5vXd433RXL/CniNqM2l4baZqg1o1dQE3C7SJiNxDKxhJWz0pKTeUnfnzezc/pDrHcETtMkMVjLSG19R/tJw2SkTkHlrLq2hNkpHukwISg5FrGI6o3bSm96sp7+P6R0REl05rPSOt91/pAyun7bcdwxG1myuz1wDb9Y84e42IqP22V1Q7XM8IsJ0wwyLstmE4okuiNXtNa30NAPIfM2evERG1j3La/hI776Naiz1mZ9p+cCX7Aiocde/eHQaDwerr8ccftzrmyJEjGDt2LKKjo5GYmIjp06ejsbHRRy0ODNmZCTYFgTGR1hMhpT9iFmcTEbWP1rR9dUCKiQzjYo9uEHBT+efPn4+HHnpI/r5Dhw7y/1ssFtxyyy3o3Lkzvv76a1RXVyMvLw9CCCxbtswXzQ0I9lbPjokMs9oNOiYyzGZ8nNP7iYic05qdpvUea65vZjByg4ALRx07dkRycrLmfZs2bcL333+PyspKpKamAgBefPFF5OfnY8GCBYiJifFmUwOKOiApa4wk5vpmm+5egAGJiMgRV9czevCGHgCs1zPie2v7BNSwGgA8//zzSEhIwLXXXosFCxZYDZmVlJSgd+/ecjACgJtuugkNDQ0oKyuz+5gNDQ0wm81WX2RLa/0jNXV3L4fYiIjsc3U9IwBcz8iNAiocPfbYY1i7di22bNmCadOmYenSpZg6dap8f1VVFZKSkqx+Ji4uDhEREaiqqrL7uAsXLkRsbKz8lZ6e7rHn4O9mqIKRvdlrDEhERI7ZC0aOpu1zPSP30H04mjdvnk2Rtfrr22+/BQDMmDEDQ4cOxTXXXIMHH3wQr7zyClauXInq6osvJIPBdhFCIYTm7ZInnngCtbW18ldlZaX7n2gAKT54CoD9vddaj2FAIiJyZHtFtcvBSPleK70HU/vpvuZo2rRpmDRpksNjunfvrnn7oEGDAAAHDhxAQkICkpOTsX37dqtjampq0NTUZNOjpGQ0GmE0GtvW8CCm3HvN0R+11v2DenC6KRERAOT0TETpodMuByNlETZdGt2Ho8TERCQmJrbrZ3ft2gUASElJAQAMHjwYCxYswIkTJ+TbNm3aBKPRiP79+7unwWR39porAYkruBIRtQ6phYYYMDM3C0uKytsUjDikdul0P6zmqpKSEhQWFuK7775DRUUF3nvvPTzyyCO49dZb0a1bNwDAqFGjcNVVV+Gee+7Brl27sHnzZsyePRsPPfQQZ6q5mXr1bEcLRHJojYjoIqnWSFlgraa10CODkfsYhBAB8VF9586dmDp1Kv73f/8XDQ0NyMjIwKRJkzBnzhxERUXJxx05cgRTp07FF198AZPJhMmTJ2Px4sVtGjYzm82IjY1FbW0tQ5UTrqzNIeEfOREFO65n5FmuXr8DJhx5E8NR22j9sRvDQtDQ3CIfI33PP3YiClb8MOl5rl6/A2ZYjfRLa4hNGYwAoKG5xWYFbQ6xEVGwsLfQozoYSUNsDEaexXBEXqEVkNS0VtBmQCKiQNeWhR6BiwGpRQgGIw9hOCKvcSUgcQVtIgombV3oUVmknZ3JpU88heGIvCo0xHb9IzUuEElEwaCtwUi6n6tgex7DEXmVpUVors2hxoBERIGsvcGIa8J5B8MReZW99Y8YkIgoWFxqMGIRtucxHJHXMSARUbBiMPIPDEfkEwxIRBSM2rOZLIOR9zEckc9cakDaXmH7hkJEpFeFReUIMRgAgMFI5xiOyKfaG5AAIMRgYO8REfkF9XAaAAYjHWM4Ip9ra0ACwOE1IvIb9uqM1BiM9IPhiHShLQGJ9UdE5C9cLcBmMNIXhiPSDVcDktabTGiIwUetJiLS1paZaQxG+sJwRLpiLyCpKe+T9hli7xER6UVbp+wD3ExWTxiOSHfUAQmA5vCaMhgt+fmNiAGJiPRAa6skZwXYADeT1QuGI9KlGblZaBGty+M7qj8CWoMR64+ISC8KFZvDtnXKPjeT1QeGI9Kt7MwEp/VHymDEgEREviYNpy1RBSQ1FmDrG8MR6Za9+qOZqjcPrqBNRHqgrjNaYuc9iMFI/8J83QAiR2bkZskhRysYSeyN7RcWlfMNh4g8qrCoHNsrqhFisK0zUgckBiP/wJ4j0j2pB0lZfM092IhID6TeotJDzmemqWuQGIz0i+GI/MIMVTBq6ya1k14rYUgiIreytyWIvQJswDogMRjpF8MR+Q1Li2j3JrWlh06zF4mI3MbRliD2CrCVRdoMRvrGcER+41I2qeUwGxG5S1sWeASs64ykgMRgpG8MR+RXLmWTWgYkIrpUlxKMpP9aWoSXW01txXBEfqctAQlgoTYRucelbAnCOiP/wnBEfokBiYi8qa3BSKtIm8HIfzAckd9ytEmtq4XaoSEGvLR5P0MSEdnV3mAk/XdQj3gGIz/DRSDJr6kXiQRs35yUtFbalpYH4IKRRKRUWFSO0BBDuzaRZW+Rf2PPEfk9qQdpUA/XC7XVwYjDbESkZG+PNAaj4GAQQrBsvo3MZjNiY2NRW1uLmJgYXzeHFNwxk4RvaETBTet9RPmBSo3vI/7D1es3e44ooLBQm4guhb0PWEuKyhmMggjDEQUcewFpZm6W5sa1DEhEBLDnmS5iOKKApA5I3LSWiBxpSzCSPmgxGAUuhiMKWFJA0iq+ZkAiIklbp+prFWkzGAUWFmS3Awuy/c+lrlPSIgSyMxP45kcUQAqLyrG9ohohhvZN1Zc+eFlaBN8b/ISr12+uc0RBQb0ekqtrISnvDzEYuBYSUYCQPjCVHjoNwPH6aFr3S3uk8f0gMHFYjYJGWzetVa+4zWE2osCg7kkGbP/mlVh4HXwYjiiotDUgAbZvjAxIRP7L3hA7AAYjkjEcUdBxx1pI3JONyP9wqj65iuGIgtKlBCTl7Df2IhHpX2FROV7avN/lPdIABqNgx9lq7cDZaoFD65MkALtvmq07bCfYLAvA2WxE+qOejab8YJMeZ0JlTZ3Nz2i9DzAYBQ5uH0LkAnUPEgCHvUjFB6ttglHxwWqUHjrNXiQiHVHORlNuAQLAaTBSF2kzGAUf9hy1A3uOAk9b1zsB+AmTSK/a2iOsvI89woGN6xwRtYH05qe1FpK93bjtzWaTHodvqETe56jomvVF5CoOqxEptHVPNoDbjhDpRVtno3GPNLKHw2rtwGG1wFdYVI7QEAMA2z3Z7L3RSnUM6mBVfPAUu+aJPEQaEs/pmQjA+u/VXm0RALsfgBiMApur12+Go3ZgOAoeba1diIkMg7m+2WYojm+6RO6n/PsEYPV3J/0tqikDE/dICz6crUbkBm2dzWaub0ZMZGspnzIYcaiNyL20tgCR/ubsBaOcngly7y5wcUjc0iIwfUQvBiOSseeoHdhzFHzaM5sN4AwYInfj3yJdCg6reRDDUfBqa8EnYFuLBIDd+ETtoB5Gu5RgxGHu4MRw5EEMR8FNKyDZm+4vUXbzswCUqG3sTZAA7C/oCNj+rTEYEcORBzEckTIgqYORvXoHgNuPELVFe7b/APhhhOxjOPIghiMCbD/NAhe77x29cSuPUxd6842bqJW9IbSZuVn4x7eVdv++OIxNjgTcbLUFCxYgJycHUVFR6NSpk+YxR44cwdixYxEdHY3ExERMnz4djY2NVsfs3r0bQ4cOhclkQteuXTF//nwwH1J7zMjNwvQRvWBpERjUI94q8ChnxGixtzQAZ7QRac9EU+6P5mjtImUwau2pjedsNGozv9k+pLGxEXfddRcGDx6MlStX2txvsVhwyy23oHPnzvj6669RXV2NvLw8CCGwbNkyAK2JMTc3F8OHD8eOHTtQXl6O/Px8REdHY9asWd5+ShQgHG09ArR+an39q0M2Q23KmgnlzwzqkYCXNu/n4pEUVJSLOYaGWM9Ek3qDnG3/waJrche/G1ZbvXo1CgoKcObMGavbP/30U4wZMwaVlZVITU0FAKxduxb5+fk4efIkYmJi8PLLL+OJJ57Ajz/+CKPRCABYtGgRli1bhqNHj8JgMLjUBg6rkT3tWZQO4OKRFNza+3eTHmfCXQPSbYq0+XdD9gTcsJozJSUl6N27txyMAOCmm25CQ0MDysrK5GOGDh0qByPpmOPHj+Pw4cPebjIFIGnRyEE94m0KQc31zUiPM2n+nLm+GRGhBpQeqtZcPHLSayUcbqOAU1hUjkmvlWgu5lh6qBrGsBCHwUgaXlPujzaoRzyDEV0yvxlWc6aqqgpJSUlWt8XFxSEiIgJVVVXyMd27d7c6RvqZqqoqZGZmaj52Q0MDGhoa5O/NZrMbW06BRvmmXGhnXzatdVkaLcLuUFvrzyTipc37WVRKfk+azBAaYkDpodMAbCczONvDUKotWlJULm8gy78Nchef9hzNmzcPBoPB4de3337r8uNpDYsJIaxuVx8jjSo6GlJbuHAhYmNj5a/09HSX20TBra3bj0gqa+oQEWrQHGZgTxL5K2VPkdRDenGD5taeImezPLn9B3mDT3uOpk2bhkmTJjk8Rt3TY09ycjK2b99udVtNTQ2amprk3qHk5GS5F0ly8uRJALDpdVJ64oknMHPmTPl7s9nMgEQum5GbhcKicrQIYbPlwczcLJQeqtb8lNxoaQ3u0lCcuq4ixGBAYVE5LwjkF6S6ImVPkdTrI/UGNTS3aP6so/XBOIRGnuDTcJSYmIjExES3PNbgwYOxYMECnDhxAikpKQCATZs2wWg0on///vIxf/jDH9DY2IiIiAj5mNTUVIchzGg0WtUpEbWV1ow25SdmwP7ikZU1dVhSVI60n4faAOthOWmIgkMKpDfK16Z6Vfnig9VIizPZXVUeuPg3Ic3inJmbxcUcySv8piD7yJEj+O6773DkyBFYLBZ89913+O6773Du3DkAwKhRo3DVVVfhnnvuwa5du7B582bMnj0bDz30kFyRPnnyZBiNRuTn52PPnj3YsGED/vSnP2HmzJkuz1QjuhTSMJvWrDRHBdsAcPTn4YaYyDCri4w0RME1kkhPpJ6iJUW22+3ERLZ+Lj/qYAgtPc4Ec32zVZE20DoMx2BEnuY3U/nz8/Px5ptv2ty+ZcsWDBs2DEBrgJo6dSq++OILmEwmTJ48GYsXL7bq9dm9ezd++9vf4ptvvkFcXBymTJmCp59+uk3hiFP5yR3s7S4OtIalsh9q7A4zhBoAi+BO46Q/9l7X0n+lniQtEaEGDOger1mfx9c1uQO3D/EghiNyp/au8SKRjtHaLoELSZI3KBdwBGy302nL65hrfZEnMRx5EMMRuZvWxUUZdly5uEh4cSFvchTuXaF8bSsnKgAM9+R+DEcexHBEnmRvw02ttZHUYiLDcFVqjM3aMVJAYuE2uculDAtLuAEzeRvDkQcxHJGnXUrdhiQi1IBGi2BdErmNO4bPWC9HvsRw5EEMR+Qt6t3J1TN+XB1qS4sz4ahit3IA7E0il2hNxwfgcI0ue9T1cdwklryN4ciDGI7ImxytFQMAg3rE4/vjZpeDEsBP7eScs95LibOQzqFe0hOGIw9iOCJfudTiVyX2JpGavV4i6TUivWbaipMESC8YjjzI2ckVQqC5uRkWi8UHrSM9CA0NRVhYmEcWF3VH3YcW9iYFL1d7iVzF5SVIrxiOPMjRyW1sbMSJEydw4cIFH7WO9CIqKgopKSnyVjWe4I7CbSX2JgUPd/cScQFH8gcMRx5k7+S2tLRg//79CA0NRefOnREREcFtSYKQEAKNjY346aefYLFY0KtXL4SEeHanHkeF25dCHZaUFzqGJf+iDENagbq9Q2ZKHD4jvWM48iB7J7e+vh4VFRXIyMhAVFSUD1tIenDhwgX88MMPyMzMRGRkpMd/n6fqRSTSzunKx2SvgP45Wo9I+W/aHhw+I3/jajgK82KbgoanewnIP3j7daC8CBUWlaNFCLfVkACQL6JpcSYUH6xG+s//BYAQg0EOZ7wo+payJk0KytJMMenfTArKlxKM7NWoSb2J00f0ctdTIvI6hiOiACQFk8KicgzqkSDXHbmjN0k6Xh2WlI+vDEscevM8da9h6aHWL/W/s/Rv1p4eRPUQq3I6vvQa478zBQqGIwLQWifzyCOP4P3330dNTQ127dqFgoICXHvttVi6dKnHfu+8efPw4Ycf4rvvvvPY7wCA7t27o6CgAAUFBR79PXrj6d4k4OKFVnoMdVjK6ZmASa+VsE7JzaQeIgA2/6bScJn073CptUT2eolYT0SBiuGIAACfffYZVq9eja1bt6JHjx5ITEzE+vXrER4e7uumucWOHTsQHR3t8vFbt27F8OHDUVNTg06dOnmuYV7kyd4kJWVYiokMs+pNUoYlABx+c4G6kBoAcnomIjTEIA+XAZDPdUxk2CUNlwHsJSJiONIZ6Y1Qa7z+pc37PfamdPDgQaSkpCAnJ0e+LT4+3u2/x1c6d+7s6ybohjd6kyTSekvKC7fycXN6JuKlzftRfPAUALB3CY5nlUlhqPTQacREWr99S+e6PWtcKbGXiAhg5bDOhIYYsKSoHC9t3m91+0ub92PJz2+a7pafn4/f/e53OHLkCAwGA7p37w4AGDZsmDwM9b//+7+IiorCO++8I//c+vXrERkZid27dwMAamtr8fDDD6NLly6IiYnBjTfeiP/85z9Wv2vRokVISkpCx44d8cADD6C+vt5h27Zu3QqDwYCNGzeib9++iIyMRHZ2tvw7JR988AGuvvpqGI1GdO/eHS+++KLV/d27d7caHjQYDHj99ddxxx13ICoqCr169cJHH30EADh8+DCGDx8OAIiLi4PBYEB+fj4A4P3330efPn1gMpmQkJCAkSNH4vz5885Psk7NyM3C2ocH4/ru8ZiZm4Xru8fbrHEEtPYkXAp7F+7XvzqEJUXlco3M+p1HseTnZQkmvVaCwp//FqT/DzSFReWY9FoJXtq8X/7/HYdPY0lROdbvPIrSQ6dtit8l5vpmm4DUHtK/rfRvrewlkl4Tax8ezGBEQYU9Rzoj9RhJ64RMH9FLDkYzPTQD5C9/+Qt69uyJ1157DTt27EBoaKjNMVdccQUWL16MqVOnYsiQIQgPD8dDDz2ERYsWoU+fPhBC4JZbbkF8fDw++eQTxMbG4tVXX8WIESNQXl6O+Ph4vPfee5g7dy7++te/4oYbbsDf//53vPTSS+jRo4fTNv7P//wP/vKXvyA5ORl/+MMfcOutt6K8vBzh4eEoKyvDhAkTMG/ePEycOBHFxcWYOnUqEhIS5FCj5ZlnnsELL7yAP//5z1i2bBnuvvtu/PDDD0hPT8cHH3yA8ePH4//+7/8QExMDk8mEEydO4Ne//jVeeOEF3HHHHTh79iy++uorBMJqGFq9SdJsJ+Di0JtUy+KONXG0VvKurKmz6l1S7hn3/XGzPAtL3dOk1xly6pljymGx4oOn5Ocn9QQpe9qUQ2P2hsna00sk/dtJ/5bS8Jk0ZFZ88BR7iSjocZ2jdnC2zpE71rWRAlFEaAgaLS0eC0aSpUuXYunSpTh8+LB827Bhw2wKsseMGQOz2YyIiAiEhITg3//+NwwGA7744gvccccdOHnyJIxGo3z8ZZddhjlz5uDhhx9GTk4O+vbti5dfflm+f9CgQaivr7dbkC3V/qxduxYTJ04EAJw+fRppaWlYvXo1JkyYgLvvvhs//fQTNm3aJP/cnDlzsHHjRuzduxeAbUG2wWDAU089hWeffRYAcP78eXTs2BGffPIJfvWrX2nWHO3cuRP9+/fH4cOHkZGR4fScuvP14EueXCfHVfa2RFEHio6RYchIiEbLz29ryvAkfe+ui76z4LP3uBmxpnA5RLryHDyJ61QRcZ0jvzd9RC8s/+IAGi0tiAgN0c2aIW+88QaysrIQEhKCPXv2yCuAl5WV4dy5c0hISLA6vq6uDgcPHgQA7Nu3D1OmTLG6f/DgwdiyZYvT3zt48GD5/+Pj43H55Zdj37598uPedtttVscPGTIES5cuhcVi0ewJA4BrrrlG/v/o6Gh07NgRJ0+etNuGvn37YsSIEejTpw9uuukmjBo1CnfeeSfi4uKctt+faRVya9UpuaM3yR5pCEkdIpTByFzfDHN9M46duThUq+x5AlqLxXccPo0fqs/Lj5mREN2u78/+/PvUvT7KIumzit+t9RzcHYzUj2dvhXMWVhM5xnCkUy9t3i8Ho0ZLC17avF8XAek///kPzp8/j5CQEFRVVSE1NRVA69YpKSkp2Lp1q83PeGq2lxTMhBA227S40iGqnolnMBjQ0tJi9/jQ0FAUFRWhuLgYmzZtwrJly/Dkk09i+/btyMzMbMcz8C/qi2hbZ71dahBw9LPOwpPk6M/DSJKzqjDV1u+VoUzNlfa4u8foqtQYObQCsBkyYxgicg3DkQ6pa4yk7wH4NCCdPn0a+fn5ePLJJ1FVVYW7774bO3fuhMlkwnXXXYeqqiqEhYXJBd1qV155JUpLS3HvvffKt5WWlrr0u0tLS9GtWzcAQE1NDcrLy3HFFVcAAK666ip8/fXXVscXFxcjKyvLbq+RM9JmsRaLxep2g8GAIUOGYMiQIXj66aeRkZGBDRs2YObMme36Pf7M1ToloLUHIy3OZNWr4m7OgoZ6CNBZL05bv29rey6V9PvVvVYzc7Pk2iEArB8iageGI53RKr7WKtL2hSlTpiA9PR1PPfUUGhsbcd1112H27Nn461//ipEjR2Lw4MG4/fbb8fzzz+Pyyy/H8ePH8cknn+D222/HgAED8NhjjyEvLw8DBgzAL37xC6xZswZ79+51qSB7/vz5SEhIQFJSEp588kkkJibi9ttvBwDMmjUL119/PZ599llMnDgRJSUlWL58OVasWNHu55qRkQGDwYCPP/4YN998M0wmE/bu3YvNmzdj1KhR6NKlC7Zv346ffvoJV155Zbt/T6DQ6lWS6n5yeiYCuPj6BbQv7J6mro1qa6+Op3t9nJF64pS9VVKvkLKuitt3EF06hiOdsbQIzeJr6XvpU7m3vfXWW/jkk0+wa9cuhIWFISwsDGvWrEFOTg5uueUW3Hzzzfjkk0/w5JNP4v7778dPP/2E5ORk/PKXv0RSUhIAYOLEiTh48CB+//vfo76+HuPHj8ejjz6Kf//7305//6JFi/DYY49h//796Nu3Lz766CO5d+e6667De++9h6effhrPPvssUlJSMH/+fIcz1Zzp2rUrnnnmGTz++OO47777cO+99+L3v/89tm3bhqVLl8JsNiMjIwMvvvgiRo8e3e7fE6i0h+Ba181S7vkl9S6pC6u1gocxLAQNzfaHPf2RveekPAdas8qkMKTsFWIYInIfzlZrB2/MVqNW/rxSNV8PjmnN9pLqZdRDYK4EI/Ux3ppJZ4+rw3ARoQY0Wi6+DUvtVs4k0/NyBUT+hLPViEjXtC7yyiJv5dR4S4vABzuPAoDV0JJEKzw5C0aXWmPkLLBpDcMpH0NafHH8dWk2yw1orRLOniEi72E4IiLdcNQrMiM3y+4+Y1J4EkIgIyEaR05fcDpT7lK/b2husen1kX5PWpwJtXVNuDo1xuVFKxl+iPSDw2rtwGE1cgVfD76j3LFevUhjiMHglnWODAaDy70+RKQPHFYjoqDl7WDCXh+iwMKNZ4mIiIgUGI48gCOVBPB1QETkrxiO3EjajuLChQs+bgnpgfQ6UG9TQkRE+saaIzcKDQ1Fp06d5M1Lo6KibPb8osAnhMCFCxdw8uRJdOrUqd1bmBARkW8wHLlZcnIyADjc3Z2CQ6dOneTXAxER+Q+GIzczGAxISUlBly5d0NTU5OvmkI+Eh4ezx4iIyE8xHHlIaGgoL45ERER+iAXZRERERAoMR0REREQKDEdERERECqw5agdpcT+z2ezjlhAREZGrpOu2s0V6GY7a4ezZswCA9PR0H7eEiIiI2urs2bOIjY21e79BcI+DNmtpacHx48fRsWNHny7yaDabkZ6ejsrKSoe7Cwcjnhv7eG4c4/mxj+fGPp4b+/R0boQQOHv2LFJTUxESYr+yiD1H7RASEoK0tDRfN0MWExPj8xecXvHc2Mdz4xjPj308N/bx3Ninl3PjqMdIwoJsIiIiIgWGIyIiIiIFhiM/ZjQaMXfuXBiNRl83RXd4buzjuXGM58c+nhv7eG7s88dzw4JsIiIiIgX2HBEREREpMBwRERERKTAcERERESkwHBEREREpMBz5gQULFiAnJwdRUVHo1KmT5jEGg8Hm65VXXrE6Zvfu3Rg6dChMJhO6du2K+fPnO91fRu9cOTdHjhzB2LFjER0djcTEREyfPh2NjY1WxwTiudHSvXt3m9fJ448/bnWMK+crUK1YsQKZmZmIjIxE//798dVXX/m6SV43b948m9dIcnKyfL8QAvPmzUNqaipMJhOGDRuGvXv3+rDFnrNt2zaMHTsWqampMBgM+PDDD63ud+VcNDQ04He/+x0SExMRHR2NW2+9FUePHvXis/AMZ+cmPz/f5nU0aNAgq2P0fG4YjvxAY2Mj7rrrLjz66KMOj1u1ahVOnDghf+Xl5cn3mc1m5ObmIjU1FTt27MCyZcuwePFiLFmyxNPN9yhn58ZiseCWW27B+fPn8fXXX2Pt2rX44IMPMGvWLPmYQD039syfP9/qdfLUU0/J97lyvgLVunXrUFBQgCeffBK7du3CDTfcgNGjR+PIkSO+bprXXX311Vavkd27d8v3vfDCC1iyZAmWL1+OHTt2IDk5Gbm5ufKek4Hk/Pnz6Nu3L5YvX655vyvnoqCgABs2bMDatWvx9ddf49y5cxgzZgwsFou3noZHODs3APCrX/3K6nX0ySefWN2v63MjyG+sWrVKxMbGat4HQGzYsMHuz65YsULExsaK+vp6+baFCxeK1NRU0dLS4uaWep+9c/PJJ5+IkJAQcezYMfm2d999VxiNRlFbWyuECPxzo5SRkSEKCwvt3u/K+QpUAwcOFFOmTLG67YorrhCPP/64j1rkG3PnzhV9+/bVvK+lpUUkJyeLRYsWybfV19eL2NhY8corr3iphb6hfo915VycOXNGhIeHi7Vr18rHHDt2TISEhIjPPvvMa233NK3rT15enrjtttvs/ozezw17jgLItGnTkJiYiOuvvx6vvPIKWlpa5PtKSkowdOhQq0W4brrpJhw/fhyHDx/2QWu9o6SkBL1790Zqaqp820033YSGhgaUlZXJxwTTuXn++eeRkJCAa6+9FgsWLLAaMnPlfAWixsZGlJWVYdSoUVa3jxo1CsXFxT5qle/s378fqampyMzMxKRJk3Do0CEAQEVFBaqqqqzOk9FoxNChQ4PuPLlyLsrKytDU1GR1TGpqKnr37h0U52vr1q3o0qULsrKy8NBDD+HkyZPyfXo/N9x4NkA8++yzGDFiBEwmEzZv3oxZs2bh1KlT8pBJVVUVunfvbvUzSUlJ8n2ZmZnebrJXVFVVyc9TEhcXh4iICFRVVcnHBMu5eeyxx3DdddchLi4O33zzDZ544glUVFTg9ddfB+Da+QpEp06dgsVisXnuSUlJAf28tWRnZ+Ott95CVlYWfvzxRzz33HPIycnB3r175XOhdZ5++OEHXzTXZ1w5F1VVVYiIiEBcXJzNMYH+uho9ejTuuusuZGRkoKKiAn/84x9x4403oqysDEajUffnhj1HPqJV9Kj++vbbb11+vKeeegqDBw/Gtddei1mzZmH+/Pn485//bHWMwWCw+l78XHCsvt3X3H1utJ6fEMLqdn85N1racr5mzJiBoUOH4pprrsGDDz6IV155BStXrkR1dbX8eK6cr0Cl9ToIhuetNHr0aIwfPx59+vTByJEjsXHjRgDAm2++KR/D83RRe85FMJyviRMn4pZbbkHv3r0xduxYfPrppygvL5dfT/bo5dyw58hHpk2bhkmTJjk8Rt2b0RaDBg2C2WzGjz/+iKSkJCQnJ9ukcamLU/3Jx9fceW6Sk5Oxfft2q9tqamrQ1NQkP29/OjdaLuV8SbNHDhw4gISEBJfOVyBKTExEaGio5usgkJ+3K6Kjo9GnTx/s378ft99+O4DWHpGUlBT5mGA8T9IMPkfnIjk5GY2NjaipqbHqITl58iRycnK822AfS0lJQUZGBvbv3w9A/+eGPUc+kpiYiCuuuMLhV2RkZLsff9euXYiMjJSntw8ePBjbtm2zqi/ZtGkTUlNTLymEeYI7z83gwYOxZ88enDhxQr5t06ZNMBqN6N+/v3yMv5wbLZdyvnbt2gUA8pu7K+crEEVERKB///4oKiqyur2oqEgXb9S+1NDQgH379iElJQWZmZlITk62Ok+NjY348ssvg+48uXIu+vfvj/DwcKtjTpw4gT179gTd+aqurkZlZaX8XqP7c+OzUnBy2Q8//CB27dolnnnmGdGhQwexa9cusWvXLnH27FkhhBAfffSReO2118Tu3bvFgQMHxN/+9jcRExMjpk+fLj/GmTNnRFJSkvj1r38tdu/eLdavXy9iYmLE4sWLffW03MLZuWlubha9e/cWI0aMEDt37hSff/65SEtLE9OmTZMfI1DPjVpxcbFYsmSJ2LVrlzh06JBYt26dSE1NFbfeeqt8jCvnK1CtXbtWhIeHi5UrV4rvv/9eFBQUiOjoaHH48GFfN82rZs2aJbZu3SoOHTokSktLxZgxY0THjh3l87Bo0SIRGxsr1q9fL3bv3i1+/etfi5SUFGE2m33ccvc7e/as/J4CQP77+eGHH4QQrp2LKVOmiLS0NPH555+LnTt3ihtvvFH07dtXNDc3++ppuYWjc3P27Fkxa9YsUVxcLCoqKsSWLVvE4MGDRdeuXf3m3DAc+YG8vDwBwOZry5YtQgghPv30U3HttdeKDh06iKioKNG7d2+xdOlS0dTUZPU4//3vf8UNN9wgjEajSE5OFvPmzfP7qerOzo0QrQHqlltuESaTScTHx4tp06ZZTdsXIjDPjVpZWZnIzs4WsbGxIjIyUlx++eVi7ty54vz581bHuXK+AtVf//pXkZGRISIiIsR1110nvvzyS183yesmTpwoUlJSRHh4uEhNTRXjxo0Te/fule9vaWkRc+fOFcnJycJoNIpf/vKXYvfu3T5sseds2bJF8/0lLy9PCOHauairqxPTpk0T8fHxwmQyiTFjxogjR4744Nm4l6Nzc+HCBTFq1CjRuXNnER4eLrp16yby8vJsnreez41BiABcBpiIiIionVhzRERERKTAcERERESkwHBEREREpMBwRERERKTAcERERESkwHBEREREpMBwRERERKTAcERERESkwHBERAEpPz8fBoMBBoMB4eHh6NGjB2bPno3z589bHffBBx9g2LBhiI2NRYcOHXDNNddg/vz5OH36tN3HXrBgAXJychAVFSXvX0hEgYPhiIgC1q9+9SucOHEChw4dwnPPPYcVK1Zg9uzZ8v1PPvkkJk6ciOuvvx6ffvop9uzZgxdffBH/+c9/8Pe//93u4zY2NuKuu+7Co48+6o2nQURexu1DiCgg5efn48yZM/jwww/l2x566CF8/PHHOHHiBL755htkZ2dj6dKleOyxx2x+/syZM057hVavXo2CggKcOXPGvY0nIp9izxERBQ2TyYSmpiYAwJo1a9ChQwdMnTpV81gOlxEFL4YjIgoK33zzDd555x2MGDECALB//3706NED4eHhPm4ZEelNmK8bQETkKR9//DE6dOiA5uZmNDU14bbbbsOyZcsAAEIIGAwGH7eQiPSI4YiIAtbw4cPx8ssvIzw8HKmpqVa9RFlZWfj666/R1NTE3iMissJhNSIKWNHR0bjsssuQkZFhE4AmT56Mc+fOYcWKFZo/yyJrouDFniMiCkrZ2dmYM2cOZs2ahWPHjuGOO+5AamoqDhw4gFdeeQW/+MUvNGexAcCRI0dw+vRpHDlyBBaLBd999x0A4LLLLkOHDh28+CyIyBMYjogoaD3//PPo378//vrXv+KVV15BS0sLevbsiTvvvBN5eXl2f+7pp5/Gm2++KX/fr18/AMCWLVswbNgwTzebiDyM6xwRERERKbDmiIiIiEiB4YiIiIhIgeGIiIiISIHhiIiIiEiB4YiIiIhIgeGIiIiISIHhiIiIiEiB4YiIiIhIgeGIiIiISIHhiIiIiEiB4YiIiIhIgeGIiIiISOH/Afbfst6sNxRJAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(2)\n",
    "fp_pcs = pca.fit_transform(finder.fixed_points['u'])\n",
    "plt.plot(fp_pcs[:, 0], fp_pcs[:, 1], 'x', label='fixed points')\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.title('Fixed points PCA')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6e1eb9ad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:49:59.242456300Z",
     "start_time": "2023-07-22T05:49:59.148606100Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fps = finder.fixed_points['u']\n",
    "plot_ids = (10, 100, 200, 300,)\n",
    "plot_ids = np.asarray(plot_ids)\n",
    "\n",
    "for i in plot_ids:\n",
    "  plt.plot(model.x, fps[i], label=f'FP-{i}')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c93e040",
   "metadata": {},
   "source": [
    "## Verify the stabilities of fixed points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9d5dd4b5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-22T05:50:00.850736200Z",
     "start_time": "2023-07-22T05:49:59.242456300Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\adadu\\miniconda3\\envs\\brainpy\\lib\\site-packages\\jax\\_src\\numpy\\array_methods.py:329: FutureWarning: The arr.split() method is deprecated. Use jax.numpy.split instead.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x200 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from jax.tree_util import tree_map\n",
    "\n",
    "_ = finder.compute_jacobians(\n",
    "  tree_map(lambda x: x[plot_ids], finder._fixed_points),\n",
    "  plot=True\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "-all",
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,auto:percent",
   "notebook_metadata_filter": "-all"
  },
  "kernelspec": {
   "display_name": "brainpy",
   "language": "python",
   "name": "brainpy"
  },
  "language_info": {
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