Dynamic Complexity of an Ivlev‐Type Prey‐Predator System with Impulsive State Feedback Control

Abstract

The dynamic complexities of an Ivlev‐type prey‐predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.