一类具有holling - IV型功能响应的时滞捕食者-猎物模型的Hopf分岔

2009 International Conference on Artificial Intelligence and Computational Intelligence Pub Date : 2009-11-07 DOI:10.1109/AICI.2009.248

Huaxiang Liu

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引用次数: 2

摘要

研究了一类具有holling - IV型功能响应的时滞捕食者-食饵模型系统。对模型的分岔分析表明，当时滞超过某一临界值时，在共存平衡点处会出现一系列Hopf分岔。利用正规形式理论和Faria和的中心流形参数，导出了确定Hopf分岔方向和分岔非平凡周期解稳定性的显式算法。最后，进行了数值模拟来证实我们的分析结果。

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Hopf Bifurcation in a Delayed Predator-Prey Model with a Holling-Type IV Functional Response

In this paper a delayed predator-prey model system with a Holling-type IV functional response is studied. The bifurcation analysis of the model shows that a sequence of Hopf bifurcations can occur at the coexisting equilibrium as the time delay crosses some critical values. An explicit algorithm for determining the direction of Hopf bifurcations and the stability of bifurcating non-trivial periodic solutions is derived by using normal form theory and center manifold arguments due to Faria and. Finally, numerical simulations are carried out to substantiate our analytical findings.

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2009 International Conference on Artificial Intelligence and Computational Intelligence

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