Combination Complex Synchronization of Fractional-Order Chaotic Complex Systems

Many researchers have made an endeavor to analyze synchronization of multi chaotic systems and present some new types of synchronization including combination synchronization [238–241], combination complex synchronization [242], combination-combination synchronization [243–246], compound synchronization [247–249], and so forth. Amongst the above-mentioned synchronization, combination complex synchronization, characterized by two scaling matrices that three chaotic systems synchronize proportionally, was proposed and studied on the basis of three integer-order chaotic complex systems with the same dimensions. The aim of this chapter is to study combination complex synchronization of fractional-order chaotic nonlinear systems. This chapter discusses the general method to realize combination complex synchronization among three commensurate fractional-order complex systems in the sense of Lyapunov in detail. Combination complex synchronization of fractional-order chaotic complex systems with incommensurate orders is investigated based on the stability theory of incommensurate fractional-order systems and active control method.