捕食者-猎物相互作用:基于Ricker模型的Allee效应

M. Y. Hamada, Tamer El-Azab, H. El-Metwally
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引用次数: 0

摘要

本文研究了受Allee效应影响的离散捕食者-猎物模型的动态特性。通过运用分岔理论和中心流形定理的严密分析,我们建立了系统局部平衡的稳定性,揭示了模型所表现出的复杂动力学行为,包括周期2、4和8的倍周期分岔,以及准周期轨道和混沌集的出现。一个值得注意的发现是参数r在塑造系统行为中所起的重要作用,因为我们通过系统地改变r而保持其他参数固定来识别一系列分岔,例如翻转和neimmark - sacker分岔。这些发现强调了模型的非线性本质,并为其复杂的动力学提供了有价值的见解。我们对这些分岔和由此产生的动力学行为的深入理解加深了我们对Allee效应对捕食者-猎物模型的影响的认识,有助于我们理解Allee效应下生态系统中种群振荡、稳定性转变和混沌动力学的出现。此外,该研究对种群管理和保护策略具有实际意义,因为将Allee效应纳入捕食者-猎物相互作用中可以更好地了解种群动态,并制定更有效和可持续的管理措施。总体而言,本文对Allee效应下的离散捕食者-猎物模型进行了综合分析,揭示了复杂的动力学行为,并强调了参数r在形成系统动力学中的影响作用,对理论认识和实际保护管理策略具有重要意义。
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Predator-Prey Interactions: Insights into Allee Effect Subject to Ricker Model
This study investigates the dynamic properties of a discrete predator-prey model influenced by the Allee effect. Through rigorous analysis utilizing bifurcation theory and the center manifold theorem, we establish the stability of the system’s local equilibrium and reveal the intricate dynamical behaviors exhibited by the model, including period-doubling bifurcations at periods 2, 4, and 8, as well as the emergence of quasi-periodic orbits and chaotic sets. A notable finding is the significant role played by the parameter r in shaping the system’s behavior, as we identify a series of bifurcations, such as flip and Neimark-Sacker bifurcations, by systematically varying r while keeping other parameters fixed. These findings underscore the non-linear nature of the model and provide valuable insights into its complex dynamics. Our enhanced understanding of these bifurcations and resulting dynamical behaviors deepens our knowledge of the Allee effect’s implications for predator-prey models, contributing to our comprehension of population oscillations, stability transitions, and the emergence of chaotic dynamics in ecological systems under the Allee effect. Moreover, this study carries practical implications for population management and conservation strategies, as incorporating the Allee effect into predator-prey interactions allows for better insights into population dynamics and the development of more effective and sustainable management practices. Overall, this comprehensive analysis of the discrete predator-prey model under the Allee effect uncovers intricate dynamical behaviors and emphasizes the influential role of the parameter r in shaping system dynamics, with implications for both theoretical understanding and practical conservation management strategies.
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期刊介绍: The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.
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