Dynamical Analysis of Prey Refuge Effects on the Stability of Holling Type III Four-species Predator-Prey System

Abstract

Models involving four species with prey refuge and type I responses have been studied with recommendations on their extension to include either type II or type III responses. However, models with Holling type II responses are de-stabilizing according to most studies. In this paper, therefore, a multi-species ecological system that includes a prey refuge and a Holling type III functional response is analyzed, to study the effect of reserved zones in enhancing the dynamical stability of the proposed system. The Routh-Hurwitz (RH) criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, 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 dynamic stability of the system.

Keywords

• Dynamical system
• Lyapunov technique
• Routh-Hurwitz criterion
• Eigenvalue approach