一类时滞捕食系统的Hopf分支(Hopf bifurcation analysis of a predator-prey system with delays)
A delayed predator-prey system with modified Leslie-Gower and Holling type IV schemes are analyzed. The local asymptotic stability and the existence of the periodic solutions via Hopf bifurcation with respect to the two delays are investigated. By analyzing the associated characteristic equation, su...
| Main Authors: | , |
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2013-11-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2013.06.002 |
| Summary: | A delayed predator-prey system with modified Leslie-Gower and Holling type IV schemes are analyzed. The local asymptotic stability and the existence of the periodic solutions via Hopf bifurcation with respect to the two delays are investigated. By analyzing the associated characteristic equation, sufficient conditions for local asymptotic stability of the positive equilibrium and the Hopf bifurcation occurring for the possible combination of the two delays are obtained. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are also presented for the support of our analytical findings. |
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| ISSN: | 1008-9497 |