Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(2): 353-373

Printed March 31, 2013

https://doi.org/10.4134/BKMS.2013.50.2.353

Copyright © The Korean Mathematical Society.

Bifurcation analysis of a delayed predator-prey model of prey migration and predator switching

Changjin Xu, Xianhua Tang, and Maoxin Liao

Central South University, Central South University, Central South University

Abstract

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.

Keywords: predator-prey model, migration, switching, stability, Hopf bifurcation

MSC numbers: 34K20, 34C25