Cluster Synchronization of Fractional-Order Nonlinearly-Coupling Community Networks With Time-Varying Disturbances and Multiple Delays

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.

Cluster synchronization of fractional‐order complex networks via variable‐time impulsive control

“…Among them, cluster synchronization refers to the phenomenon that all dynamic nodes are divided into several clusters in the networks, which belong to the same cluster can reach complete synchronization, while those in different clusters are always desynchronized. In fact, according to the function of the networks, its specific goals need to be divided into different types, so the cluster synchronization of the networks has been popularly concerned [19][20][21][22][23][24][25]. In the past few decades, researchers have realized cluster synchronization of fractional-order complex networks by designing different controllers.…”

“…In the past few decades, researchers have realized cluster synchronization of fractional‐order complex networks by designing different controllers. For example, [21] has studied the cluster synchronization problem of fractional‐order complex networks with internal delay and coupled delay, and added adaptive pinning controller to all subnetworks of each cluster to achieve cluster synchronization with isolated nodes. In [24], the cluster synchronization problem of coupled fractional‐order neural networks via feedback control has been discussed.…”

“…In recent years, fractional calculus has been introduced into complex dynamic networks, which further improves the design, expression, and control ability of complex dynamic networks. Moreover, complex dynamic networks often exhibit some complex and interesting dynamic behaviors, including consensus [13], flocking [14], and synchronization [15][16][17][18][19][20][21][22][23][24][25].…”

“…Synchronization is a kind of cooperative behavior in the networks, which refers to the process that multiple subsystems influence each other through information interaction, and all subsystems eventually tend to the same state. According to different performance characteristics, synchronization can be classified as projection synchronization [15], exponential synchronization [16,17], bipartite synchronization [18], cluster synchronization [19][20][21][22][23][24][25], and so on. Among them, cluster synchronization refers to the phenomenon that all dynamic nodes are divided into several clusters in the networks, which belong to the same cluster can reach complete synchronization, while those in different clusters are always desynchronized.…”