diff --git a/docs/4-tutorials.md b/docs/4-tutorials.md index 60d6d628..7d24299a 100644 --- a/docs/4-tutorials.md +++ b/docs/4-tutorials.md @@ -1066,17 +1066,17 @@ Species competition models explore how interspecific interactions, such as compe A discrete-time model for a three-species predator-prey competition can be complex, but here's a basic version using a system of difference equations. Let's denote the populations of the three species at time \f$t\f$ as \f$𝑃_1(t)\f$, \f$P_2(t)\f$ and \f$P_3(t)\f$. Assume that \f$P_1\f$ is a prey species, \f$P_2\f$ is a predator of \f$P_1\f$ and \f$P_3\f$ is a competing species that preys on \f$P_1\f$ and competes with \f$P_2\f$. -\f$$ +\f[ P_1(t+1) = P_1(t) + r_1 P_1(t) \left(1 - \frac{P_1(t)}{K_1}\right) - a_{12} P_1(t) P_2(t) - a_{13} P_1(t) P_3(t) -\f$$ +\f] -\f$$ +\f[ P_2(t+1) = P_2(t) + r_2 P_2(t) \left(1 - \frac{P_2(t)}{K_2}\right) + b_{21} P_1(t) P_2(t) - c_{23} P_2(t) P_3(t) -\f$$ +\f] -\f$$ +\f[ P_3(t+1) = P_3(t) + r_3 P_3(t) \left(1 - \frac{P_3(t)}{K_3}\right) + b_{31} P_1(t) P_3(t) - c_{32} P_2(t) P_3(t) -\f$$ +\f] Where: - \f$ r_1, r_2, r_3 \f$ are the intrinsic growth rates of species 1, 2, and 3, respectively.