Oscillations for a delayed predator–prey model with Hassell–Varley-type functional response - 10/04/15
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Abstract |
In this paper, a delayed predator–prey model with Hassell–Varley-type functional response is investigated. By choosing the delay as a bifurcation parameter and analyzing the locations on the complex plane of the roots of the associated characteristic equation, the existence of a bifurcation parameter point is determined. It is found that a Hopf bifurcation occurs when the parameter τ passes through a series of critical values. The direction and the stability of Hopf bifurcation periodic solutions are determined by using the normal form theory and the center manifold theorem due to Faria and Maglhalaes (1995). In addition, using a global Hopf bifurcation result of Wu (1998) for functional differential equations, we show the global existence of periodic solutions. Some numerical simulations are presented to substantiate the analytical results. Finally, some biological explanations and the main conclusions are included.
Le texte complet de cet article est disponible en PDF.Keywords : Predator-prey model, Hassell–Varley functional response, Stability, Hopf bifurcation
Plan
☆ | This work is supported by National Natural Science Foundation of China (No. 11261010 and No. 60902044), the Doctoral Foundation of Guizhou College of Finance and Economics (2010), the Science and Technology Program of Hunan Province (No. 2010FJ6021) and the soft Science and Technology Program of Guizhou Province (No. 2011LKC2030). |
Vol 338 - N° 4
P. 227-240 - avril 2015 Retour au numéroBienvenue sur EM-consulte, la référence des professionnels de santé.
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