Bifurcation and Chaos Control for Prey Predator Model with Step Size in Discrete Time

Abstract

The Lotka – Volterra systems served as a basis for the development and analysis of more realistic mathematical models of nonlinear interactions. A new form of discrete time 2-D prey predator model involving Lesile - Gower functional response with step size is proposed for discussion. Utilizing Euler scheme, discrete system is obtained from the continuous dynamical system. Dynamical consistency of the model which includes the existence and stability of the fixed points is investigated. Eigenvalues of Jacobian matrix are computed for corresponding fixed points. Analytical results illustrate rich dynamics and complexity of the model. The bifurcation theory is employed to study the existence of flip and Neimark-Sacker bifurcations. The chaos control of the discrete system is performed and numerical simulations are provided supporting the results.