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

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.