Discrete-Time Predator–Prey System Incorporating Fear Effect: Stability, Bifurcation, and Chaos Control

• Qamar Din ^[1] ; Khansa Jameel ^[1] ; Muhammad Sajjad Shabbir ^[1]
  1. [1] University of Poonch Rawalakot
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01145-2
• Enlaces
  • Texto completo
• Resumen

  • In predator–prey interactions, the effect of fear is an important factor in building ecological communities, affecting biodiversity, and maintaining ecological balance. In this paper, we present a specific predator–prey model that incorporates the effects of fear on prey populations by focusing on non-overlapping generations. Our study aims to explore the existence of biologically feasible equilibrium points and to analyze local asymptotic behavior around these points. Furthermore, using the center manifold theorem and the normal form theory of bifurcations, we study period-doubling bifurcations about prey-free and interior (positive) fixed points. On the other hand, the Neimark-Sacker bifurcation around the positive equilibrium point is investigated by applying the bifurcation theory of normal forms. We study the existence of chaos and present effective strategies to control the fluctuating and chaotic behaviors in the system using various chaos control techniques. Numerical simulations are presented to illustrate the theoretical discussion.

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