Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model

Abstract

Abstract We investigate the dynamical behavior of a modified Leslie–Gower prey–predator model with harvesting in prey population. In order to explore rich dynamics of the model, Euler approximation is implemented to obtain a discrete-time modified Leslie–Gower model. Existence of equilibria and their local asymptotic stabilities are carried out. Furthermore, with the help of bifurcation theory and center manifold theorem, existence and directions of period-doubling and Neimark–Sacker bifurcations are investigated at positive steady-state. In order to control chaos and bifurcations, the Ott–Grebogi–Yorke (OGY) method and the hybrid control strategy are introduced. Numerical simulations are also provided to illustrate the theoretical discussions.

Keywords

• Modified Leslie–Gower model
• Stability analysis
• Period-doubling bifurcation
• Neimark–Sacker bifurcation
• Chaos control