Dynamical Analysis of Prey Refuge Effects on the Stability of Holling Type III Four-species Predator-Prey System

IF 3.2 Q3 Mathematics Results in Control and Optimization Pub Date : 2024-02-16 DOI:10.1016/j.rico.2024.100390

Odhiambo Francis, Titus Aminer, Benard Okelo, Julius Manyala

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Abstract

Models involving four species with prey refuge and type I responses have been studied with recommendations on their extension to include either type II or type III responses. However, models with Holling type II responses are de-stabilizing according to most studies. In this paper, therefore, a multi-species ecological system that includes a prey refuge and a Holling type III functional response is analyzed, to study the effect of reserved zones in enhancing the dynamical stability of the proposed system. The Routh-Hurwitz (RH) criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, global stabilities have been studied using the Lyapunov technique. Numerical simulations have been carried out using the Matlab ode45 solver software to verify the analytical results. The findings show that refuge plays a significant part in improving the dynamic stability of the system.

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猎物避难所对霍林 III 型四种捕食者-猎物系统稳定性影响的动力学分析

研究了四个物种的猎物避难所和 I 型响应模型，并建议将其扩展到 II 型或 III 型响应。然而，根据大多数研究，霍林 II 型响应模型会失去稳定性。因此，本文分析了一个包含猎物避难所和霍林 III 型功能响应的多物种生态系统，以研究保留区对提高拟议系统动态稳定性的影响。在研究局部稳定性时，采用了 Routh-Hurwitz 准则和特征值技术。另一方面，利用 Lyapunov 技术研究了全局稳定性。为验证分析结果，使用 Matlab ode45 求解器软件进行了数值模拟。研究结果表明，避难所在提高系统动态稳定性方面发挥了重要作用。

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