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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December 2024
Research Article|
December 09 2024
Dispersal induced catastrophic bifurcations, Arnold tongues, shrimp structures, and stock patterns in an ecological system
Special Collection:
From Sand to Shrimps: In Honor of Professor Jason A. C. Gallas
Rajni
;
Rajni
a)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
Differential Equations, Modeling and Simulation Group, Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh
, India
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Bapan Ghosh
Bapan Ghosh
b)
(Conceptualization, Formal analysis, Funding acquisition, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – review & editing)
Differential Equations, Modeling and Simulation Group, Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh
, India
b)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
b)Author to whom correspondence should be addressed: [email protected]
a)
Electronic mail: [email protected]
Chaos 34, 123139 (2024)
Article history
Received:
September 27 2024
Accepted:
November 14 2024
Citation
Rajni, Bapan Ghosh; Dispersal induced catastrophic bifurcations, Arnold tongues, shrimp structures, and stock patterns in an ecological system. Chaos 1 December 2024; 34 (12): 123139. https://doi.org/10.1063/5.0240974
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