Partial Synchronizability Characterized by Principal Quasi-Submatrices Corresponding to Clusters

Abstract EN

A partial synchronization problem in an oscillator network is considered.

The concept on a principal quasi-submatrix corresponding to the topology of a cluster is proposed for the first time to study partial synchronization.

It is shown that partial synchronization can be realized under the condition depending on the principal quasi-submatrix, but not distinctly depending on the intercluster couplings.

Obviously, the dimension of any principal quasi-submatrix is usually far less than the one of the network topology matrix.

Therefore, our criterion provides us a novel index of partial synchronizability, which reduces the network size when the network is composed of a great mount of nodes.

Numerical simulations are carried out to confirm the validity of the method.