Adaptive pinning cluster synchronization of fractional-order complex dynamical networks

The problem about cluster synchronization of fractional-order CDNs is studied via a pinning adaptive approach in this paper. Based on the stability theory of fractional differential equations, some sufficient criteria for local and global cluster synchronization of fractional-order CDNs are derived. In this paper, the coupling configuration matrix can be asymmetric as well as reducible and the inner coupling matrix can also be asymmetric. Moreover, the number of pinning nodes in each cluster can be evaluated. Especially, when the coupling strength is large enough and the coupling configuration matrix is symmetric, cluster synchronization can be achieved via pinning a single node in each cluster. Finally, some typical examples are given to illustrate the correctness and effectiveness of our results, a surprising finding is that the synchronization performance will become better as the fractional order decreases in this simulation.