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BIFURCATION ANALYSIS OF A DELAYED PREDATOR-PREY MODEL OF PREY MIGRATION AND PREDATOR SWITCHING
Xu, Changjin,Tang, Xianhua,Liao, Maoxin Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
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.
Bifurcation analysis of a delayed predator-prey model of prey migration and predator switching
Changjin Xu,Xianhua Tang,Maoxin Liao 대한수학회 2013 대한수학회보 Vol.50 No.2
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.