Complex dynamics for a discretized fractional-order predator-prey system with constant-yield prey harvesting and fear effect

Dengfeng Wang; Xianyi Li; Xiao Zhu; Enrui Zhang; Dengfeng Wang; Xianyi Li; Xiao Zhu; Enrui Zhang

doi:10.3934/mmc.2025021

Mathematical Modelling and Control

2025, Volume 5, Issue 3: 305-320. doi: 10.3934/mmc.2025021

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Research article

Complex dynamics for a discretized fractional-order predator-prey system with constant-yield prey harvesting and fear effect

Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received: 23 January 2025 Revised: 01 April 2025 Accepted: 24 May 2025 Published: 13 August 2025
39A28, 39A30

In this paper, we derived and studied the discrete version of a continuous fractional-order predator-prey system with constant-yield prey harvest and a monotonically increasing function response, as well as a fear effect of the predator on the bait. After studying in detail the existence and local stability of the fixed points of the system, some favorable conditions for the occurrence of its Neimark–Sacker bifurcation and period-doubling bifurcation were obtained by using the central manifold theorem and bifurcation theory. Finally, numerical simulations carried out using Matlab software illustrate the theoretical results previously obtained and reveal its some new dynamics–the chaotic occurrence.
- Caputo fractional derivative,
- discrete predator-prey system,
- Neimark–Sacker bifurcation,
- period-doubling bifurcation
Citation: Dengfeng Wang, Xianyi Li, Xiao Zhu, Enrui Zhang. Complex dynamics for a discretized fractional-order predator-prey system with constant-yield prey harvesting and fear effect[J]. Mathematical Modelling and Control, 2025, 5(3): 305-320. doi: 10.3934/mmc.2025021

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Abstract

In this paper, we derived and studied the discrete version of a continuous fractional-order predator-prey system with constant-yield prey harvest and a monotonically increasing function response, as well as a fear effect of the predator on the bait. After studying in detail the existence and local stability of the fixed points of the system, some favorable conditions for the occurrence of its Neimark–Sacker bifurcation and period-doubling bifurcation were obtained by using the central manifold theorem and bifurcation theory. Finally, numerical simulations carried out using Matlab software illustrate the theoretical results previously obtained and reveal its some new dynamics–the chaotic occurrence.

References

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