A Novel Discrete-Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey with Allee effect in predator’s population, whose dynamics are analyzed explored. We have determined equilibrium points studied their local stability properties. find that undergoes flip bifurcation Neimark–Sacker around interior point by choosing parameter parameter. discuss direction of both bifurcations help normal form theory center manifold theorem. most common routes orbit Moreover, we utilize state feedback, pole placement, hybrid control methods chaos work is complete numerical simulations confirm analytical findings.