Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers

Abstract

The objective of this paper is to investigate the synchronization for nonlinear time-delayed coupling complex dynamic networks with different dimensional nodes through the use of decentralized dynamic compensation controllers. We propose a nonlinear time-delayed coupling complex dynamic network model with similar nonlinear nodes, whose dimensions admit differences. For this kind of network model, based on Barbalat's lemma, decentralized dynamic compensation controllers are designed for the state synchronization of the coupled nodes under some mathematical conditions. In addition, the synchronization manifold is defined as an invariant manifold, which is regarded as the generalized case of the networks with the same node dynamics. Finally, numerical examples with chaotic and hyperchaotic nodes are presented to verify the effectiveness of our theoretical results.

Synchronization of Complex Dynamical Networks with Dynamical Behavior Links

“…where 1 i ∈  m×n , i = 1, 2, … , N, are the controller gain matrices to be designed. By considering the matrix Kronecker product, the synchronization error dynamic system (8) can be written as the following form:…”

Delay-dependent H∞ filtering for complex dynamical networks with time-varying delays in nonlinear function and network couplings

“…Nowadays, various control methods such as adaptive control, sample data control, impulsive control, H ∞ control have been explored to realize the synchronization phenomena of CDNs, for details see [11,13,19] and references therein. The sample data controller has been applied in [20,21] to synchronize the CDNs with Markovian jump parameters by considering the time-varying delays in the network.…”

“…The dynamical behavior of CDNs with non-identical nodes are much more complicated than with identical nodes. To deal with different dimensional nodes, authors in [19] have studied the synchronization criteria for time-delayed coupling CDNs with different dimensional nodes by using the decentralized dynamic compensation controllers.…”

Pinning Control of the Coupled Distributed Parameter System with Time Delay

“…The dynamical analysis of coupled system has become a focal topic, particularly the synchronization phenomena. Some results on synchronization in various coupled lump parameter systems have been given in [26][27][28][29][30][31][32][33]. Although synchronization of the coupled LPS is studied popularly, synchronization of the coupled DPS is only investigated in [22] and [23].…”