Abstract
This paper investigates the adaptive cluster synchronization of fractional-order complex networks with internal and coupling delays as well as time-varying disturbances via the fractional-order hybrid controllers. To be more practical, the unknown disturbances and dynamical behaviors of nodes are assumed to be nonidentical. Based on the properties of fractional calculus and the fractional-order comparison principle, sufficient conditions are derived to guarantee the cluster synchronization of two kinds of fractional-order nonlinear dynamical systems, which extends the results in existing literatures. Numerical simulations are presented to show the effectiveness of our theoretical results.
Highlights
Complex networks are ubiquitous in the real world, such as the World Wide Web, transportation networks, gene networks, economic networks, etc
Pan et al investigated the cluster synchronization of stochastic dynamical systems with time delay, and the estimation of cluster decay was obtained based on an impulsive control technique in [7]
Internal delay, nonlinearly-coupling delays, and unknown disturbances widely exist in the real networks, which makes their influences on the dynamic behaviors of neural networks cannot be ignored
Summary
Complex networks are ubiquitous in the real world, such as the World Wide Web, transportation networks, gene networks, economic networks, etc. Some important and interesting results have been obtained for cluster synchronization of complex dynamical systems with fractional-order calculus. Wang et al [25] investigated project cluster synchronization of fractional-order complex networks with coupling time-varying delays and identical nodes by designing an integer-order feedback controller. In [28], based on the fractional stability theory, the authors investigated local and global cluster synchronization in fractional-order dynamical systems with asymmetric coupling matrix via using fractional-order adaptive pinning control. Internal delay, nonlinearly-coupling delays, and unknown disturbances widely exist in the real networks, which makes their influences on the dynamic behaviors of neural networks cannot be ignored. Inspired by the motivations above, this paper investigates cluster synchronization of fractional-order complex networks with internal delay and nonlinearly-coupling delay as well as unknown time-varying.
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