Abstract
This paper studies the cluster synchronization of a kind of complex networks by means of impulsive pinning control scheme. These networks are subject to stochastic noise perturbations and Markovian switching, as well as internal and outer time-varying delays. Using the Lyapunov-Krasovskii functional, Itö’s formula, and some linear matrix inequalities (LMI), several novel sufficient conditions are obtained to guarantee the desired cluster synchronization. At the end of this writing, a numerical simulation is given to demonstrate the effectiveness of those theoretical results.
Highlights
Introduction and Model DescriptionComplex networks can be used to describe properly many biological, social, and communication systems and are made up of a great number of nodes representing individuals or organizations and links that are employed to mimic the interactions among them [1]
A lot of different synchronization patterns have been investigated such as complete synchronization [9], phase synchronization [10], partial synchronization [11], and cluster synchronization [12]
The cluster synchronization can be understood as the dynamical nodes synchronize each other in each group, while there is no synchronization between any two different groups
Summary
Complex networks can be used to describe properly many biological, social, and communication systems and are made up of a great number of nodes representing individuals or organizations and links that are employed to mimic the interactions among them [1]. Discrete Dynamics in Nature and Society discussed a class of coupled neural networks with stochastic noise and intermittent control. Their Wiener processes were of a vector form that can be viewed as an improvement of [18]. Recurring to linear matrix inequality, [21] considered the synchronization of a class of complex networks with Markovian jumping parameters whose coupling configuration was not dependent on mode switching. In view of the preceding discussion, this paper will focus on the issue of the synchronization of stochastic complex networks with Markovian switching and time-varying delay coupling by impulsive pinning control method.
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