STABILITY AND BIFURCATION ANALYSIS OF A PREDATOR-PREY SYSTEM UNVEILING THE ROLE OF PREY REFUGE AND COOPERATION WITH FADING MEMORY

Parvaiz Ahmad Naik; Ramesh K; Ranjith Kumar G; Sania Qureshi

doi:10.11948/20240561

2026 Volume 16 Issue 1

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Parvaiz Ahmad Naik, Ramesh K, Ranjith Kumar G, Sania Qureshi. STABILITY AND BIFURCATION ANALYSIS OF A PREDATOR-PREY SYSTEM UNVEILING THE ROLE OF PREY REFUGE AND COOPERATION WITH FADING MEMORY[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 99-120. doi: 10.11948/20240561

Citation:

Parvaiz Ahmad Naik, Ramesh K, Ranjith Kumar G, Sania Qureshi. STABILITY AND BIFURCATION ANALYSIS OF A PREDATOR-PREY SYSTEM UNVEILING THE ROLE OF PREY REFUGE AND COOPERATION WITH FADING MEMORY[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 99-120. doi: 10.11948/20240561

STABILITY AND BIFURCATION ANALYSIS OF A PREDATOR-PREY SYSTEM UNVEILING THE ROLE OF PREY REFUGE AND COOPERATION WITH FADING MEMORY

1.
School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, Sichuan, China
2.
Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise 533000, Guangxi, China
3.
Department of Mathematics, Anurag University, Venkatapur, Hyderabad-500088, Telangana, India
4.
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
5.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia, Mersin 10, Turkey
6.
Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan

Author Bio: Email: ranjithreddy1982@gmail.com(R. K. G); Email: sania.shahid@lau.edu.lb(S. Qureshi)
Corresponding authors: Email: naik.parvaiz@ymun.edu.cn(P. A. Naik); Email: krameshrecw@gmail.com(R. K)

Abstract

Abstract

This paper explores the impact of prey group cooperation on predator-prey dynamics through a novel mathematical model incorporating a Caputo fractional derivative and gestation delay. Solutions' existence, uniqueness, and boundedness of solutions are verified within the framework. The stability analysis indicates that the coexistence equilibrium point is globally stable and that periodic oscillations are caused by the Hopf bifurcation. Our results reveal a critical link between model order, prey refuge rate, and cooperation level. As the model order decreases or the prey refuge rate and cooperation level diminish, the system transitions from unstable to stable behavior. These findings suggest that while strong memory (represented by a higher model order) hinders stable coexistence, weaker memory (lower order) can promote it. This study highlights the significance of incorporating memory effects and prey behavior into predator-prey models for a more comprehensive understanding of population dynamics.
- Caputo derivative /
- stability /
- existence and uniqueness /
- time-delay /
- Hopf bifurcation
MSC: 26A33,37C75,34C23,34A12

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References

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