Graph-theoretic approach to synchronizing stochastic coupled systems with time-varying delays on networks via periodically intermittent control
Section snippets
introduction
Over the past decades, coupled system on networks (CSNs), as a special kind of complex networks, have been studied extensively because they have many important applications in various areas such as moving image processing, optimization, speed detection of moving subjects, secure communication and so on, see [1], [2], [3], [4] and references therein. Especially, the synchronization phenomena in CSNs have secured growing attention among the research community since the fact that synchronization
Preliminaries and model formulation
In this section, we first introduce some basic notations and a vital lemma in graph theory. Then, we give the model formulation and finally present two important definitions.
Main results
In this section, we consider the IES problem of system (1) under periodically intermittent control (3). Some IES criteria for system (1) will be derived by combing Lyapunov method with graph theory.
An application to stochastic coupled oscillators with time-varying delays
Synchronization of oscillators model is extensively studied in physical and biological systems for underlying interests ranging from novel communications strategies to understand how large and small neural assemblies efficiently and sensitively achieve desired functional goals. In this section, we will apply the main results to discuss IES of stochastic coupled oscillators with time-varying delays. Firstly, a common oscillator reads where φ ≥ 0 is the dimpling
Numerical Test
In this section, we provide an example with numerical simulation to demonstrate the effectiveness of the proposed theoretical results.
Here we proceed to consider the IES problem of stochastic coupled oscillators (30) under periodically intermittent control. Take system (30) can be expressed by a digraph and the coupling strengths dik, hik and mik are shown as follows:
Conclusion
In this paper, we have studied IES of SCSTDNs via periodically intermittent control. By combining graph theory with Lyapunov method, several simple yet generic sufficient conditions for IES of SCSTDNs under periodically intermittent control have been derived. As illustrations, the IES analysis of stochastic coupled oscillators with time-varying delays has been carried out by applying the derived theoretic results. A numerical simulation has been given to show the effectiveness of the
Acknowledgment
The authors are very grateful to the reviewers for carefully reading the paper and for their valuable comments and suggestions which have improved the paper.
References (37)
- et al.
Global-stability problem for coupled systems of differential equations on networks
J. Differ. Equ.
(2010) - et al.
Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control
Appl. Math. Comput.
(2018) - et al.
Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control
Appl. Math. Comput.
(2017) - et al.
Synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control
Appl. Math. Comput.
(2017) - et al.
Novel approaches to pin cluster synchronization on complex dynamical networks in Lure forms
Commun. Nonlinear Sci. Numer. Simul.
(2018) - et al.
State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties
Appl. Math. Comput.
(2018) - et al.
Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control
Phys. Lett. A
(2011) - et al.
Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control
Neural Netw.
(2014) - et al.
Finite-time stability and stabilization for ITÔ-type stochastic markovian jump systems with generally uncertain transition rates
Appl. Math. Comput.
(2018) - et al.
Graph theory-based approach to boundedness of stochastic Cohen-Grossberg neural networks with markovian switching
Appl. Math. Comput.
(2013)