Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

Abstract

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

Existence and stability of periodic solution of a Lotka–Volterra predator–prey model with state dependent impulsive effects

“…For example [10] established the conditions for the existence and stability of periodic solution of population dynamic with birth pulses, [9,16,19,22,[27][28][29]32] studies the dynamical behavior of epidemic model with pulse vaccination, and [18,20,21,[24][25][26]31,33,34] researched the population models with impulsive effects and devoted to the criteria for the existence, stability, orbital stability of periodic solutions.…”

Dynamic complexities of a predator–prey model with generalized Holling type III functional response and impulsive effects

“…Therefore, a reasonable model describing this phenomena is a predator-prey model with impulses. Recently, such models have been studied by many researchers; to name a few, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein. We should mention that impulses may cause very complex dynamics.…”

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

“…Various types of functional responses in predator-prey dynamic system such as Monod-type, semi-ratiodependent and Holling-type have been studied. [1] is an example for the study about Holling-type functional re-sponse. In this paper, we consider the predator-prey system with Beddington DeAngelis type functional response and impulses.…”