From the point of view of secure communication, more unpredictable scaling factors can additionally enhance the security. In this paper, a new type of chaotic synchronization (mixed function projective synchronization called in this paper) is proposed, whereby the response system specifically has a scaling factor matrix and the drive system has a scaling function matrix. The mixed function projective synchronization is a generalization of many existing projection synchronization schemes, such as the function projective synchronization and the modified projective synchronization and so on. To achieve the mixed function projective synchronization between chaotic systems with fully uncertain parameters, a general mathematical method for designing the controllers is proposed based on the stability analysis and the adaptive control technique. To demonstrate the validity, the proposed method is applied to the synchronization of an integer-order chaotic system and a fractional-order chaotic Chen system.
