Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

Al-Kaff, Mohammed O.; El-Metwally, Hamdy A.; Elsadany, Abd-Elalim A.; Elabbasy, Elmetwally M.

doi:10.1038/s41598-024-62439-8

Sci Rep

2024

DOI: 10.1038/s41598-024-62439-8

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Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

Mohammed O. Al-Kaff,

Hamdy A. El-Metwally,

Abd-Elalim A. Elsadany

et al.

Abstract: This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic b… Show more

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2024

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Cited by 2 publications

References 29 publications

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

Rajni,

Ghosh

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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

Rajni,

Ghosh

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mathematical exploration on control of bifurcation for a 3D predator-prey model with delay

Zhao,

Xu,

et al. 2024

MATH

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<p>In this current paper, we developed a new predator-prey model accompanying delay based on the earlier works. By applying inequality strategies, fixed point theorem, and a suitable function, we got new necessary conditions for the existence, uniqueness, nonnegativeness, and boundedness of the solution to the developed delayed predator-prey model. The bifurcation behavior and stability nature of the defined delayed predator-prey model were investigated by using stability and bifurcation theory of delayed differential equations. We have modified the Hopf bifurcation's appearance time and stability domain by building two distinct hybrid delayed feedback controllers for the delayed predator-prey model. The time of Hopf bifurcation appearance and stability domain of the model were explored. Matlab experiment diagrams were given to support the learned important results. The derived outcomes in this paper were original and have significant theoretical implications for maintaining equilibrium between the densities of the three species.</p>

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Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

Cited by 2 publications

References 29 publications

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

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

Mathematical exploration on control of bifurcation for a 3D predator-prey model with delay

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