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.

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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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