Abstract
A Lotka–Volterra predator–prey model incorporating predator cannibalism is proposed and studied in this paper. The existence and stability of all possible equilibria of the system are investigated. Our study shows that cannibalism has both positive and negative effect on the stability of the system, it depends on the dynamic behaviors of the original system. If the predator species in the system without cannibalism is extinct, then suitable cannibalism may lead to the coexistence of both species, in this case, cannibalism stabilizes the system. If the cannibalism rate is large enough, the prey species maybe driven to extinction, while the predator species are permanent. If the two species coexist in the stable state in the original system, then predator cannibalism may lead to the extinction of the prey species. In this case, cannibalism has an unstable effect. Numeric simulations support our findings.
Highlights
1 Introduction The aim of this paper is to investigate the dynamic behaviors of the following predator– prey model with cannibalism for predator: dx
Based on the traditional Lotka–Volterra predator–prey model, we propose and study a predator–prey model with predator cannibalism in this paper
We have investigated the local and global stability of the possible equilibria of the model
Summary
The aim of this paper is to investigate the dynamic behaviors of the following predator– prey model with cannibalism for predator: dx. Deng et al Advances in Difference Equations (2019) 2019:359 decade, many scholars investigated the dynamic behaviors of the predator–prey species, see [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40] and the references therein.
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