Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect

Parvaiz Ahmad Naik; Muhammad Amer; Rizwan Ahmed; Sania Qureshi; Zhengxin Huang; Parvaiz Ahmad Naik; Muhammad Amer; Rizwan Ahmed; Sania Qureshi; Zhengxin Huang

doi:10.3934/mbe.2024201

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 4554-4586. doi: 10.3934/mbe.2024201

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Research article Special Issues

Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect

1.
Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise 533000, China
2.
Department of Mathematics, Air University Multan Campus, Multan, Pakistan
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon
4.
Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Pakistan
5.
Department of Mathematics, Near East University, Mersin, Turkey

Received: 21 September 2023 Revised: 27 January 2024 Accepted: 01 February 2024 Published: 28 February 2024

The refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as period-doubling and Neimark-Sacker (NS) bifurcations. The bifurcating and fluctuating behavior of the system was controlled via feedback and hybrid control methods. In addition, numerical simulations were performed as evidence to back up our theoretical findings. According to our findings, maintaining an optimal level of refuge availability was critical for predator and prey population cohabitation and stability.
- predator-prey system,
- Ricker,
- refuge,
- stability,
- period-doubling bifurcation,
- Neimark-Sacker (NS) bifurcation,
- chaos control
Citation: Parvaiz Ahmad Naik, Muhammad Amer, Rizwan Ahmed, Sania Qureshi, Zhengxin Huang. Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 4554-4586. doi: 10.3934/mbe.2024201

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Abstract

The refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as period-doubling and Neimark-Sacker (NS) bifurcations. The bifurcating and fluctuating behavior of the system was controlled via feedback and hybrid control methods. In addition, numerical simulations were performed as evidence to back up our theoretical findings. According to our findings, maintaining an optimal level of refuge availability was critical for predator and prey population cohabitation and stability.

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