The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response

Abstract

In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.

Bifurcationing Analysis of Predator-Prey Diffusive System Based on Bazykin Functional Response

“…In ecology, population A is called predator and population B is called predator, and together they form a predator-prey system. The predator-prey system has a long and distinguished history in applied mathematics as a classical mathematical system for the study of predator-prey systems, which is originated from the exploration of chemical reactions [1] and biological interactions [2] and has been widely studied for its rich kinetic behavior [3] [4] [5] [6].…”