Numerical Analysis of Prey Refuge Effects on the Stability of Holling Type III Four-Species Predator-Prey System

The dynamic behavior of a multi-species system that includes a prey refuge and a Holling type III functional response is examined in this work. The pre-requisites for the presence of the equilibrium points, as well as their local and global stabilities, for the suggested system are analyzed and derived. The Routh-Hurwitz criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, the global stabilities have been studied using the Lyapunov technique. Numerical simulations have been carried out using the Matlab ode45 solver software to verify the analytical results. The findings show that refuge plays a significant part in improving the dynamical stability of the system.