Elsevier

Applied Mathematics Letters

Volume 62, December 2016, Pages 42-48
Applied Mathematics Letters

Global dynamics of a predator–prey model with defense mechanism for prey

https://doi.org/10.1016/j.aml.2016.06.013Get rights and content
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Abstract

Recently, Venturino and Petrovskii proposed a general predator–prey model with group defense for prey species (Venturino and Petrovskii, 2013). The local dynamics had been studied and showed that the model might undergo Hopf bifurcation, and have an extinction domain. In this paper, we dedicate ourselves to the investigation of the global dynamics of the model by establishing the conditions of the nonexistence of periodic orbits, and the existence and uniqueness of limit cycles.

Keywords

Predator–prey model
Defense mechanism
Extinction domain
Limit cycle
Global dynamics

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Research is supported by the National Natural Science Foundation of China (11271260), Shanghai Leading Academic Discipline Project (XTKX2012), Hujiang Foundation of China (B14005), and the Innovation Program of Shanghai Municipal Education Commission (13ZZ116).