Study of a Predator-Prey Model with Holling Type IV Functional Response

Abstract

Population ecology, is an important branch in ecology. The problem of mutual restriction between populations has been the focus of research in recent years. The interaction between populations can be represented by a function called a functional response function. According to different populations, the functional response functions are also divided into many categories. This article studies a predator-prey model with Holling type IV functional response, which is more in line with actual conditions. From a biological point of view, this paper divides the population into three major groups, namely prey, susceptible predator and infected predator. The local stability analysis of the ecosystem around the steady state near the biological feasible equilibrium point was carried out, and the global stability analysis of the model was carried out by using the Lyapunov function. Finally, Matlab software was used to carry out numerical simulation of the analysis results.