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

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 n...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-11, Vol.23 (Suppl 1), Article 285
Main Authors: Din, Qamar, Jameel, Khansa, Shabbir, Muhammad Sajjad
Format: Article
Language:English
Subjects:
Asymptotic properties
Bifurcation theory
Biological effects
Canonical forms
Centre manifold theory
Chaos theory
Control systems
Difference and Functional Equations
Discrete time systems
Dynamical Systems and Ergodic Theory
Ecological effects
Fear
Fixed points (mathematics)
Mathematics
Mathematics and Statistics
Predator-prey simulation
Predators
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01145-2