Synchronization analysis of drive-response multi-layer dynamical networks with additive couplings and stochastic perturbations

Abstract

This paper concerns the synchronization of a kind of drive-response multi-layer dynamical networks with additive couplings and stochastic perturbations. Multi-layer networks are a kind of complex networks with different layers, which consist of different kinds of interactions or multiple subnetworks. Additive couplings are designed to capture the different layered connections. In this paper, two pinning controllers are designed to guarantee the synchronization of the stochastic multi-layer network. One is the state-feedback pinning controller with constant control gains. The other one is the adaptive pinning controller with adaptive control gains. It is worthwhile to mention that our assumptions on the activation functions satisfy a generalized Lipschitzian condition which are weaker than those in the previous works. Moreover, as we prove, only selected part of the nodes to be controlled are enough to guarantee that the drive system and response network can be stochastically synchronized. Finally, an example and its simulations are presented to show the feasibility effectiveness of our control schemes.

Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control

“…In addition, there is also outer synchronization, which refers to synchronization between different complex networks. The outer synchronization researches in complex networks can be found in the literature [12][13][14]. For the outer synchronization of the single-layer networks, Wang et al [12] studied the synchronization between two delay-coupled complex dynamical networks with a noise perturbation using an adaptive controller.…”

“…Hymavathi et al [13] introduced an outer synchronization scheme for fractional-order neural networks with time delays, and derived several criteria achieving synchronization between the drive and response systems based on fractional inequalities and Lyapunov-type functions. Zhuang et al [14] used drive-response methods to study the synchronization of multi-layer dynamical networks with additive delay couplings and stochastic perturbations, and obtained sufficient conditions for synchronization between the drive and response networks using pinning controllers. In the existing work of outer synchronization in complex networks, one usually designs some suitable control protocols to drive the synchronization of networks.…”

Synchronization Analysis for Stochastic Inertial Memristor-Based Neural Networks with Linear Coupling

“…As we know, noise plays an important role in synchronization since it can stabilize an unstable system. In recent years, many scholars are very interested in synchronization of stochastic networks with time-varying delays [2,[29][30][31][32][33][34][35][36][37][38]. In 2013, the Jensen integral inequality was improved by the so-called Wirtinger-based integral inequality [33].…”

“…Furthermore, Gao et al [29] showed that a state feedback controller and an adaptive updated law used to guarantee stochastic memristor-based neural networks with noise disturbance can be asymptotically synchronized. In [38], the authors investigated the synchronization of a stochastic multilayer dynamic network with time-varying delays and additive couplings by designing two pinning controllers.…”

Synchronization for a class of complex-valued memristor-based competitive neural networks(CMCNNs) with different time scales

“…In recent years, neurals networks have attracted a lot of researchers in different research areas [20,21,4,27,7,8]. It is worth mentioning that MCNNs with different time scales, which are extensions of conventional neural networks.…”