Dispersal induced catastrophic bifurcations, Arnold tongues, shrimp structures, and stock patterns in an ecological system.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0240974
Rajni, Bapan Ghosh
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引用次数: 0

Abstract

This paper presents a comprehensive analysis of a discrete-time predator-prey model within a homogeneous two-patch environment, incorporating both prey and predator dispersal. We consider a logistic growth for both prey and predator species, and the predation process is based on the Holling type-II functional response in the isolated patches. We explore the existence of multiple coexisting equilibria and establish their stability conditions. By independently varying the prey and predator dispersal rates, we discover a sequence of phenomena including bifurcations, quasiperiodicity, and chaos. In addition, we observe a 10-period orbit, each point of the periodic orbit gives birth to a closed invariant curve. Such large number of closed invariant curves are generally not reported in spatially coupled population models. The system exhibits both catastrophic (non-smooth) jumps and smooth transitions in the dynamics whenever a bifurcation occurs. Commonly, dispersal can only destabilize the coexisting equilibrium. However, we found the stabilization of the coexisting equilibrium, which is a rare occurrence. Furthermore, a two-parameter space analysis reveals intricate dynamics when both dispersal rates are varied simultaneously, showcasing complex phenomena and the emergence of organized periodic regimes such as Arnold tongues and shrimp structures. We also investigate the stock pattern of both species with respect to the dispersal. This study enhances the understanding of predator-prey interactions in spatially homogeneous environments, illuminating their intricate and dynamic nature.

扩散导致生态系统的灾难性分叉、阿诺德舌、虾结构和种群模式。
本文综合分析了均匀双斑块环境下的离散时间捕食者-猎物模型,考虑了猎物和捕食者的分散。我们考虑了猎物和捕食者物种的逻辑增长,并且捕食过程基于孤立斑块的Holling ii型功能响应。我们探讨了多个共存平衡点的存在性,并建立了它们的稳定性条件。通过独立地改变猎物和捕食者的扩散速率,我们发现了包括分岔、准周期性和混沌在内的一系列现象。另外,我们观察到一个10周期的轨道,周期轨道的每一点都产生一条闭合不变曲线。如此大量的闭不变曲线在空间耦合的种群模型中通常没有报道。当分岔发生时,系统在动力学中表现出灾难性(非平滑)跳跃和平滑过渡。通常,分散只会破坏共存的平衡。然而,我们发现了共存平衡的稳定化,这是罕见的。此外,双参数空间分析揭示了两种扩散速率同时变化时的复杂动力学,显示了复杂的现象和有组织的周期机制的出现,如阿诺德舌和虾结构。我们还研究了两种物种的种群分布模式。本研究增强了对空间同质环境中捕食者-猎物相互作用的理解,阐明了其复杂和动态的本质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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