Hopf bifurcation in a predator-prey system with Holling type III functional response and time delays |
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| Authors: | Zizhen Zhang Huizhong Yang Ming Fu |
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| Affiliation: | 1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, 214122, P.R. China
2. School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030, P.R. China
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| Abstract: | This paper is concerned with a delayed predator-prey system with modified Leslie-Gower and Holling type III schemes. By analyzing the associated characteristic equation, its local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. Based on the normal form method and center manifold theorem, the formulaes for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, some numerical simulations to illustrate the theoretical analysis are also carried out. |
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