Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

Abstract

This paper focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays. Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities. These criteria rely on system parameters alone and can be used conveniently in practical applications. In addition, the system parameters do not satisfy the conditions of the proposed criteria. That is, the system itself cannot synchronize. However, system synchronization can be achieved by adding the appropriate feedback controllers, thereby providing a practical and effective control method for complex dynamical networks. An estimation method of exponential convergence rate is also presented. Finally, the effectiveness of the proposed criteria is verified through numerical simulations.

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

“…Synchronization, as a major feature of complex networks, has attracted considerable attention. At present, many different styles of synchronization, such as complete [4], global [5], cluster [6], lag [7], exponential [8], and finite-time synchronization [9], are available.…”

Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event‐Triggered Control: The Threshold Function Method

“…However, there are some networks that cannot be synchronized by their own internal structure; thus, some controllers have been designed to force them to synchronize. Some works have investigated the synchronization of the complex dynamical networks via control strategies in recent years [15][16][17][18]. For example, in [19], the problem of synchronization control of complex dynamical networks subject to nonlinear couplings and uncertainties has been investigated.…”

Intermittent Control for Cluster‐Delay Synchronization in Directed Networks

“…Based on the two methods mentioned above, many other surveys have been carried out to explore the mysterious mechanisms of chaos synchronization and chaos control. As the study develops in depth, various kinds of synchronization protocols have been put forward and deeply studied, such as complete synchronization [5], exponential synchronization [6,7], projective synchronization [8,9], lag synchronization [10], and cluster synchronization [11][12][13]. The above-mentioned results only discussed synchronization induced by mutual coupling and the intrinsic structure of the network.…”