Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

Abstract EN

This paper studies the synchronization of complex dynamical networkswith multilinks and similar nodes.

The dynamics of all the nodes inthe networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations.

Networks withsimilar nodes are universal in the real world.

In order to depictthe similarity of the similar nodes, we give the definition of theminimal similarity of the nodes in the network for the first time.

We find the threshold of the minimal similarity of the nodes in thenetwork.

If the minimal similarity of the nodes is bigger than thethreshold, then the similar nodes can achieve synchronizationwithout controllers.

Otherwise, adaptive synchronization method isadopted to synchronize similar nodes in the network.

Some newsynchronization criteria are proposed based on the Lyapunov stabilitytheory.

Finally, numerical simulations are given to illustrate thefeasibility and the effectiveness of the proposed theoreticalresults.