Complex modified generalized projective synchronization of fractional-order complex chaos and real chaos

This paper introduces a type of modified generalized projective synchronization with complex transformation matrix (CMGPS) for fractional-order complex chaos and real chaos with the same dimension and different structures. The transformation matrix in this type of chaos synchronization is a non-diagonal square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, necessary and sufficient criteria are established to guarantee CMGPS for the fractional-order complex chaos and fractional-order real chaos, and for two fractional-order complex chaotic systems, respectively. Numerical examples are provided to illustrate the feasibility and effectiveness of our theoretical results.