Bifurcation analysis and chaos control of discrete prey–predator model incorporating novel prey–refuge concept

Abstract

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period-doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge-based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long-term chaotic behavior over a broad range of parameters.