GitHub - a-granados/PO_periodic_systems: Computation of periodic orbits of non-autonomous systems and fixed points of maps using Newton method

These routines compute the initial conditions for a periodic orbit of a non-autonomous with periodic dependence on time:

$\displaystyle \dot{x}=f(x,t),\quad f(x,t+T)=f(x,t).$

That is, the goal is to compute a point

such that, for a given

,

$\displaystyle \varphi(t_0+qT;x)=x.$

The method used consists on performing a Newton method to solve the equation

$\displaystyle S_{t_0}(x)-x=0,$

where $S_{t_0}$ is the stroboscopic map (time

return map):

$\displaystyle S_{t_0}(x)=\varphi(t_0+qT;x)$

The program needs the gsl libraries, and can be compiled using

g++ -o main main.c rk78.c lu.c memory.c -lgsl -lgslcblas

Name		Name	Last commit message	Last commit date
Latest commit History 18 Commits
README.md		README.md
img1.png		img1.png
img2.png		img2.png
img3.png		img3.png
img4.png		img4.png
img5.png		img5.png
img6.png		img6.png
img7.png		img7.png
img8.png		img8.png
lu.c		lu.c
lu.h		lu.h
main.c		main.c
memory.c		memory.c
memory.h		memory.h
rk78.c		rk78.c
rk78.h		rk78.h

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