Conformable Fractional Order Lotka-Volterra Predator-Prey Model: Discretization, Stability and Bifurcation

Abstract

The purpose of this study is to discuss dynamic behaviors of conformable fractional-order Lotka-Volterra predator-prey system. First of all, the piecewise constant approximation is used to obtain the discretize version of the model then, we investigate stability, existence, and direction of Neimark-Sacker bifurcation of the positive equilibrium point of the discrete system. It is observed that the discrete system shows much richer dynamic behaviors than its fractional-order form such as Neimark-Sacker bifurcation and chaos. Finally, numerical simulations are used to demonstrate the accuracy of analytical results. © 2019 by ASME.