Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

Abstract

This paper is concerned with a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects. By using the fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model, which completes some results given in recent years. Further, by applying the comparison theorem in impulsive differential equations and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples and numerical simulations are given to illustrate the feasibility and effectiveness of the main results. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamics of a diffusive predator–prey model with herd behavior

“…In population dynamics, the functional response refers to the number of prey eaten per predator per unit time as a function of prey density. Generally, the functional response can be classified into many different types, such as Holling I-IV types [10,11,16,19], Hassell-Varley type [9], Beddington-DeAngelis type [3,6], Crowley-Martin type [5], Leslie-Gower type [13] and so on, and have been proposed and investigated widely [2,7,15,18,20,21,25,31,32].…”