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首页> 外文期刊>WSEAS Transactions on Business and Economics >Qualitative Analysis in A Predator-prey Model with Sigmoidal Type Functional Response
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Qualitative Analysis in A Predator-prey Model with Sigmoidal Type Functional Response

机译：具有S型功能反应的捕食者-食饵模型的定性分析。

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摘要

In this paper, a cyclic predator-prey system with Sigmoidal type functional response is considered. The stability of the positive equilibrium and existence of Hopf bifurcation is studied by analyzing the distribution of the roots of associated characteristic equation. It is shown that the positive equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of the positive equilibrium will cause a bifurcating periodic solution as the time delay passes through a sequence of critical values. An explicit formula for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations is derived, using the normal form theory and center manifold argument. Finally, numerical simulations supporting the theoretical results are carried out.
机译：本文考虑具有S形函数响应的循环捕食者-被捕食系统。通过分析相关特征方程根的分布来研究正平衡的稳定性和Hopf分支的存在。结果表明，当时间延迟足够小时，正平衡是局部渐近稳定的，而当时间延迟通过一系列临界值时，正平衡的稳定性变化将导致分岔的周期解。利用范式理论和中心流形参数，导出了确定从Hopf分支分支的Hopf分支周期解的稳定性和方向的明确公式。最后，进行了支持理论结果的数值模拟。

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