Complex dynamics of a discretized Rosenzweig–MacArthur prey-predator model with fear effect on prey and prey refuge

Md. Jasim Uddin; Md. Mutakabbir Khan; Ibraheem M. Alsulami; Amer Alsulami; Md. Jasim Uddin; Md. Mutakabbir Khan; Ibraheem M. Alsulami; Amer Alsulami

doi:10.3934/math.2025659

AIMS Mathematics

2025, Volume 10, Issue 6: 14629-14656. doi: 10.3934/math.2025659

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Research article

Complex dynamics of a discretized Rosenzweig–MacArthur prey-predator model with fear effect on prey and prey refuge

1.
Department of Mathematics, University of Dhaka, Dhaka-1000, Dhaka, Bangladesh
2.
Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
3.
Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia

Received: 12 April 2025 Revised: 14 June 2025 Accepted: 18 June 2025 Published: 26 June 2025
MSC : 40A05, 70K50, 92D25

This work explores a discrete-time predator-prey system governed by a prey-dependent Rosenzweig–MacArthur response, incorporating the fear effect in prey dynamics. The study examines equilibrium properties and bifurcation mechanisms, particularly near the interior fixed point, highlighting their ecological significance. Various bifurcation types, including period-doubling and Neimark-Sacker, are identified, with precise conditions ensuring the latter's occurrence. To manage the system's intricate behavior, Ott-Grebogi-Yorke (OGY) and state feedback control are implemented. Numerical simulations reinforce theoretical findings through phase space reconstructions, Lyapunov exponent analysis, bifurcation diagrams, and local stability assessments, offering a comprehensive perspective on system transitions and control strategies.
- prey-predator model,
- codimension-1 bifurcations,
- fear-effect,
- refuge,
- chaos control
Citation: Md. Jasim Uddin, Md. Mutakabbir Khan, Ibraheem M. Alsulami, Amer Alsulami. Complex dynamics of a discretized Rosenzweig–MacArthur prey-predator model with fear effect on prey and prey refuge[J]. AIMS Mathematics, 2025, 10(6): 14629-14656. doi: 10.3934/math.2025659

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Abstract

This work explores a discrete-time predator-prey system governed by a prey-dependent Rosenzweig–MacArthur response, incorporating the fear effect in prey dynamics. The study examines equilibrium properties and bifurcation mechanisms, particularly near the interior fixed point, highlighting their ecological significance. Various bifurcation types, including period-doubling and Neimark-Sacker, are identified, with precise conditions ensuring the latter's occurrence. To manage the system's intricate behavior, Ott-Grebogi-Yorke (OGY) and state feedback control are implemented. Numerical simulations reinforce theoretical findings through phase space reconstructions, Lyapunov exponent analysis, bifurcation diagrams, and local stability assessments, offering a comprehensive perspective on system transitions and control strategies.

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