Hidden Attractors, Chaos Control and Synchronization in Two Fractional Systems Governed by Caputo–Fabrizio Derivatives

Abstract

Two 3D systems that involve Caputo–Fabrizio fractional derivatives are discussed. A necessary and sufficient condition for achieving the local stability of an equilibrium state of a general 3D system is introduced. All the equilibria are used to stabilize the systems’ chaotic states using suitable linear feedback control gains. Chaos synchronization is obtained in the two 3D systems using suitable linear control functions. An adequate numerical scheme is used to discretize and simulate the two chaotic systems governed by Caputo–Fabrizio operators. Hence, varieties of complex dynamics are illustrated such as one‐scroll attractors, hidden periodic attractors, self‐excited and hidden chaotic attractors. Moreover, the bifurcation diagrams and attraction basins are carried out to simulate and illustrate the varieties of such chaotic dynamics, and hidden quasi‐periodic and chaotic attractors.