Stability Analysis of a Discrete-Time Predator–Prey Model Using Piecewise Constant Argument

This paper offers a thorough analysis of the discrete-time predator–prey model obtained by using the piecewise constant argument technique. Our principal findings demonstrate that the coexistence fixed exhibits rich dynamical behavior, undergoing both Neimark–Sacker and period-doubling bifurcations as ecological parameters vary. These bifurcations lead to the emergence of quasiperiodic oscillations and chaotic dynamics, which pose significant threats to population persistence. To address this challenge, we develop a hybrid control strategy that effectively stabilizes the system by suppressing chaotic behavior and restoring predictable population dynamics. Numerical simulations confirm the efficacy of our control approach across different parameter regimes. The study provides ecologists with a practical methodology: employing bifurcation analysis to identify instability thresholds followed by targeted control intervention to maintain ecological stability, with particular relevance for managing vulnerable or harvested species.