Complicate dynamical analysis of a discrete predator-prey model with a prey refuge

A. Q. Khan; Ibraheem M. Alsulami; A. Q. Khan; Ibraheem M. Alsulami

doi:10.3934/math.2023768

AIMS Mathematics

2023, Volume 8, Issue 7: 15035-15057. doi: 10.3934/math.2023768

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Complicate dynamical analysis of a discrete predator-prey model with a prey refuge

A. Q. Khan ^{1
,
,},
Ibraheem M. Alsulami ²

1.
Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2.
Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Received: 12 January 2023 Revised: 01 April 2023 Accepted: 12 April 2023 Published: 23 April 2023
MSC : 70K50, 92D25, 40A05

In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model.
- chaos,
- discrete model,
- bifurcations,
- refuge,
- numerical simulation
Citation: A. Q. Khan, Ibraheem M. Alsulami. Complicate dynamical analysis of a discrete predator-prey model with a prey refuge[J]. AIMS Mathematics, 2023, 8(7): 15035-15057. doi: 10.3934/math.2023768

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Abstract

In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model.

References

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