Stability, bifurcations and chaotic dynamics in a delayed hybrid tri-trophic food chain model with Holling type-Ⅱ and Leslie-Gower type functional responses

Chandrima Banerjee; Pritha Das; A. B. Roy

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Stability, bifurcations and chaotic dynamics in a delayed hybrid tri-trophic food chain model with Holling type-Ⅱ and Leslie-Gower type functional responses

机译：具有Holling-Ⅱ型和Leslie-Gower型功能性反应的时滞混合三营养食物链模型的稳定性，分叉和混沌动力学

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In this paper the qualitative behaviour of a delayed tri-trophic food chain model with Holling type Ⅱ and modified Leslie-Gower functional responses is studied. Condition for existence and local stability of the interior equilibrium of the model are derived. Hopf bifurcation analysis is discussed by considering gestation time delay as bifurcation parameter. Applying normal form method and center manifold theory, the direction and stability of the bifurcating periodic solutions are determined. Analytical findings are verified by numerical results.

机译：研究了具有HollingⅡ型和改进的Leslie-Gower功能反应的时滞三营养食物链模型的定性行为。推导了模型内部平衡的存在条件和局部稳定性。通过将妊娠时间延迟作为分叉参数来讨论Hopf分叉分析。应用范式和中心流形理论，确定了分叉周期解的方向和稳定性。数值结果验证了分析结果。

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来源
《World journal of modelling and simulation》 |2015年第3期|174-198|共25页
作者
Chandrima Banerjee; Pritha Das; A. B. Roy;
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作者单位

Department of Mathematics, Techno India, Salt Lake, Sector- V, Kolkata-700091, India;

Department of Mathematics, I.I.E.S.T, Shibpur, Howrah - 711103, India;

Department of Mathematics, Jadavpur University, Kolkata-700032, India;

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正文语种 eng
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关键词
Tri-trophic food chain; Leslie-Gower type functional response; Hopf bifurcation; chaos; Lya-punov exponent;

机译：三营养食物链;Leslie-Gower型功能性反应;Hopf分叉;混沌;Lya-punov指数;

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1. Dynamical complexities in a tri-trophic hybrid food chain model with Holling type II andCrowley–Martin functional responses [J] . R.K. Upadhyay, S.N. Raw, V. Rai Nonlinear Analysis : Modelling and Control . 2010,第3期

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Stability, bifurcations and chaotic dynamics in a delayed hybrid tri-trophic food chain model with Holling type-Ⅱ and Leslie-Gower type functional responses

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