Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

Abstract

This article is concerned with the problem of synchronization in nonlinear complex networks with multiple time-varying delays via adaptive aperiodically intermittent control. The couplings inside nodes are assumed to be nonlinear and subject to multiple time-varying delays. Meanwhile, the connection topology among the nodes can be directed and weighted. Then, the adaptive aperiodically intermittent control method is employed to realize synchronization and automatic modification to compensate the changes in dynamic errors.In addition, several synchronization criteria are rigorously induced based on the Lyapunov stability theory. Finally, the proposed control method is evaluated by utilizing numerical simulation. The results can be also applied to linear complex networks with delays.

Pinning synchronization of nonlinear hybrid‐coupled complex networks with double time delays via aperiodically intermittent adaptive control

“…Remark The problem of the synchronization for nonlinear hybrid‐coupled system () was considered by applying adaptive controller to each node in Reference 37. For large‐scale networks, it is uneconomical or almost impossible to impose the controller on all the nodes.…”

“…In some common network systems such as biological systems, coupled memristive neural networks and secure communications, one node often makes its own state change with the current and historical information of its neighbors simutaneously. [35][36][37] Additionally, in many cases, the state of the node may not be directly perceived by others. 38,39 So realistic modeling of dynamical networks should require all of them mentioned above to be taken into account.…”

“…Remark It is well known that there generally exist two types of time delay in dynamical networks: one is internal self‐feedback delay due to the peculiarities of dynamical nodes, and the other is coupling delay caused by finite information transmission speed among nodes. In some common network systems such as biological systems, coupled memristive neural networks and secure communications, one node often makes its own state change with the current and historical information of its neighbors simutaneously 35‐37 . Additionally, in many cases, the state of the node may not be directly perceived by others 38,39 .…”

“…Remark The synchronization of nonlinear complex networks with multiple delays was studied via adaptive aperiodically intermittent control in Reference 37. In this reference, the authors only considered the coupling delay in the system, but did not pay attention to the internal self‐feedback delay of dynamical nodes.…”

Finite-Time Synchronization and Identification between Two Nonlinear Coupled Multiweighted Markovian Switching Delayed Networks with Uncertain Models and External Disturbances

“…erefore, the synchronization of nonlinear coupled systems also has great research value, and the results are more practical. In [14], the authors concerned with the problem of synchronization in nonlinear complex networks with multiple time-varying delays via adaptive aperiodic intermittent control. In [4], the authors dealt with the problem for synchronization of a nonlinear time-delayed complex spatiotemporal network (CSN), modeled by semilinear parabolic partial differentialdifference equations.…”