Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes

This paper investigates a new hybrid projective synchronization scheme between two coupled fractional-order complex networks with different sizes. The hybrid projective synchronization studied in this paper includes complete synchronization of the states of the nodes in each network and projective synchronization of the states of a pair of nodes from both networks. Based on the stability theorem of fractional-order differential system and adaptive control technique, some sufficient conditions for guaranteeing the existence of the hybrid projective synchronization are derived. Two examples are given to show the effectiveness of the proposed methods.