Nonlinear dynamics and chaos in Caputo-like discrete fractional Chen system

Abstract

In this paper, a fractional Caputo-difference form of discrete Chen system is introduced. The considered system is proposed by implementing the fractional Caputo-like difference operator instead of the standard forward difference operator in the linearized form of the Chen system. The dynamics of the suggested discrete system are numerically illustrated for different fractional orders using phase plots, bifurcation diagrams and Lyapunov exponents. Double scroll chaotic attractors for the considered system are displayed. This study confirms the possible existence of chaos in Caputo-like discrete fractional systems.