Complex Modified Projective Synchronization of Fractional-Order Chaotic Complex Systems

Complex modified projective synchronization (CMPS) is a new type of complex synchronization based on complex chaotic systems that was proposed almost simultaneously in 2013 [163, 164]. CMPS means that state variables of the master system converge to state variables of the slave system with a complex constant scaling matrix [224, 225]. In this chapter, we first investigates CMPS of the commensurate fractional-order chaotic complex systems by combining stability results of the fractional-order systems and the pole placement method. Subsequently,CMPS 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.