Finite-Time Adaptive Cluster Synchronization of Heterogeneous Fractional-Order Dynamic Networks with Community Structure and Co-Competition Interactions

This paper is devoted to investigating the problem of finite-time (FnT) adaptive cluster synchronization for heterogeneous fractional-order dynamic networks (FODNs) with community structure and co-competition interactions. By designing a suitable adaptive controller and using reduction to absurdity, some sufficient conditions are derived to ensure the considered heterogeneous FODNs can achieve cluster synchronization over a FnT interval. Meanwhile, the cluster-synchronized setting times (CSSTs) are evaluated effectively by means of the monotonicity of the Mittag-Leffler function. It is indicated that the estimated CSSTs are associated with the order of the derivation and the control parameters. Finally, numerical simulations are carried out to validate the effectiveness of our theoretical results.