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.
Changjin Xu, Xianhua Tang, and Maoxin Liao
Central South University, Central South University, Central South University
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
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