Combinatorial synchronization of complex multiple networks with unknown parameters

Abstract

In this paper, a combinatorial inner synchronization within a sub-network, which consists of four-wing chaotic system with unknown parameters and external disturbances as node dynamics, and a combinatorial outer synchronization between different sub-networks are investigated. Based on the Lyapunov stability theory, LaSalle's invariance principle, cluster analysis, and pinning control technique, some sufficient conditions, which can ensure not only the combinatorial inner synchronization of the nodes with identical node dynamics in a sub-network, but also the combinatorial outer synchronization of the sink nodes with identical or nonidentical ones between different sub-networks by a suitable switch control scheme, are obtained. By using the pinning control, only the sink node within a sub-network which has direct connections to the sink nodes in other sub-networks needs to be controlled. Finally, some numerical simulations are presented to demonstrate the feasibility and validity of the obtained results by taking the star-like topological structure as an example.

Order parameter analysis of synchronization transitions on star networks

“…Understanding the intrinsic microscopic mechanism embedded in collective macroscopic behaviors of populations of coupled units on heterogenous networks has become a focus in a variety of fields, such as the biological neurons circadian rhythm, chemical reacting cells, and even society systems [1][2][3][4][5][6][7][8]. Numerous different emerging macroscopic states/phases have been revealed, and various non-equilibrium transitions among these states have been observed and studied on heterogenous networks [9][10][11][12][13][14][15][16][17][18][19].…”

Cluster synchronization on multiple sub-networks of complex networks with nonidentical nodes via pinning control

“…Synchronization, as one of the most important and interesting collective behavior of complex dynamical networks, has been studied extensively due to its ubiquity in many system models, such as the large-scale complex dynamical networks [4,5], smallworld neuronal networks [6,7], scale-free neuronal networks [8,9], and potential applications in many other areas, including information science, secure communication, and biological systems. Up to now, many different kinds of synchronization patterns including complete synchronization [10], global synchronization [11], stochastic synchronization [12], combinatorial synchronization [13,14], and cluster synchronization [15] have been proposed. In the case where the whole network cannot synchronize by its intrinsic structure, some control schemes may be designed to drive the network to synchronization.…”