在捕食者疾病循环的捕食者-猎物系统中,阿利和恐惧在控制混乱中的作用

K. Das, Anirban Patra, Seema Sarkar, Rajinder Pal Kaur, Biswadip Pal, Md Firoj Ali, Sayantari Ghosh, Somnath Sikari
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引用次数: 0

摘要

本文利用霍林 II 型功能反应的罗森茨韦格-麦克阿瑟模型,探讨了捕食者-猎物系统中捕食者种群的恐惧和疾病问题。主要重点是研究恐惧因素的影响,即捕食者引起的恐惧会阻碍猎物的生长速度。此外,该模型还考虑了疾病在捕食者之间的传播,从而导致易感和受感染的捕食者亚群的划分。在易感捕食者中加入阿利效应进一步丰富了模型。该研究进行了全面审查,包括局部和全局稳定性分析,以及内部平衡点周围的霍普夫分岔分析。数值模拟强调了一个值得注意的观察结果:相互作用力的升级推动系统进入混沌动力学,其特点是稳定焦点、极限循环和周期加倍现象。一个值得注意的发现是阿利参数([公式:见正文])对混沌动力学的影响。随着阿利参数值的增加,系统通过一系列混沌状态、周期加倍和极限循环趋于稳定聚焦。随后,论文在混沌动力学中引入了另一个关键参数--恐惧因子的作用。耐人寻味的是,通过各种非线性现象,包括周期加倍和极限循环,混沌状态转化为稳定焦点。这种对参数的细微探索揭示了捕食者-猎物系统错综复杂的动力学规律,让我们对恐惧、疾病和生态因素之间的相互作用有了全面的了解。因此,我们在本文中观察到,在逐一注入我们的新特征:恐惧因子和阿利参数后,混沌在这里是如何表现的?
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Role of Allee and Fear for Controlling Chaos in a Predator–Prey System with Circulation of Disease in Predator
This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey’s growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter ([Formula: see text]) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter?
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