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首页> 外文期刊>Advances in Difference Equations >Analysis of stability and Hopf bifurcation in a fractional Gauss-type predatora??prey model with Allee effect and Holling type-III functional response
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Analysis of stability and Hopf bifurcation in a fractional Gauss-type predatora??prey model with Allee effect and Holling type-III functional response

机译：具有Allee效应和Holling III型功能反应的分数高斯型捕食者食饵模型的稳定性和Hopf分支分析。

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摘要

The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predatora??prey model that includes the Allee effect and Holling type-III functional response. Instead of using classic first order differential equations to formulate the model, fractional order differential equations are utilized. The existence and uniqueness of a nonnegative solution as well as the conditions for the existence of equilibrium points are provided. We then investigate the local stability of the three types of equilibrium points by using the linearization method. The conditions for the existence of a Hopf bifurcation at the positive equilibrium are also presented. To further affirm the theoretical results, numerical simulations for the coexistence equilibrium point are carried out.
机译：Kolmogorov模型已应用于许多生物学和环境问题。我们对其变体之一特别感兴趣，即包括Allee效应和Holling III型功能性反应的Gauss型捕食者??猎物模型。代替使用经典的一阶微分方程来公式化模型，而是利用分数阶微分方程。提供了非负解的存在性和唯一性以及平衡点存在的条件。然后，我们使用线性化方法研究三种类型的平衡点的局部稳定性。还提出了在正平衡处存在霍普夫分支的条件。为了进一步肯定理论结果，对共存平衡点进行了数值模拟。

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