Dynamical analysis of discretized Logistic model with Caputo-Fabrizio fractional derivative

Abstract

In this paper we consider a fractional order Logistic model with Caputo-Fabrizio fractional derivative. By applying two-step Adams-Bashforth scheme, we obtain a system of difference equations. By using the SchurCohn criterion, stability conditions of the positive equilibrium point of the discrete system are obtained. It is observed that the discrete system shows much richer dynamic behaviors than its fractional-order form such as Neimark-Sacker bifurcation and chaos. The direction and stability of the Neimark-Sacker bifurcation are determined by using the normal form and center manifold theory. In addition, the effect of fractional order parameter on the dynamical behavior of the system is investigated. Finally, numerical simulations are used to demonstrate the accuracy of analytical results.