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Stability and bifurcation analysis of a delayed predator-prey model of prey dispersal in two-patch environments
Authors:Changjin Xu  Xianhua Tang  Maoxin Liao
Institution:a School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410083, PR China
b Faculty of Science, Hunan Institute of Engineering, Xiangtan 411004, PR China
c School of Mathematics and Physics, Nanhua University, Hengyang 421001, PR China
Abstract:In this paper, a class of delayed predator-prey model of prey dispersal in two-patch environments is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae 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 simulation for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.
Keywords:Predator-prey model  Dispersion  Stability  Hopf bifurcation  Periodic solution
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