Cluster modified projective synchronization between community networks

Abstract

Cluster modified projective synchronization of two community networks with nonidentical nodes is studied in this paper. Each network has a unique dynamics and its clusters have different parameter sets which could make their dynamics chaotic or periodic for instance. Therefore, we are dealing with varieties of dynamics in these clusters. By introducing an adaptive control gain in our controller design and using Lyapunov stability theory, we show that two community networks can reach to the synchronized state having arbitrary matrix scaling factor between corresponding nodes of the networks. Moreover, using this matrix we can observe different synchronization regimes simultaneously in each pair of corresponding nodes.