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Almost Sure Synchronization of Multilayer Networks via Intermittent Pinning Noises: A White-Noise-Based Time-Varying Coupling
IEEE Transactions on Circuits and Systems I: Regular Papers ( IF 5.1 ) Pub Date : 2021-06-07 , DOI: 10.1109/tcsi.2021.3082005
Sen Li , Yuhang Zheng , Huan Su

This paper is concerned with the almost sure exponential synchronization of a multilayer network which is set up on a non-strongly connected digraph that can be classified into several layers by Tarjan’s algorithm. Note that, in the multilayer network, white-noise-based time-varying coupling and drift term coupling are proposed to simulate two kinds of coexisting distinguishable interactions between vertices. We develop a normal analytical framework for studying synchronization of the multilayer network. Firstly, via aperiodically intermittent pinning noises, synchronization of vertices situated on the first layer is achieved in the layered network. Secondly, under the impact of the white-noise-based time-varying coupling in diffusion term, synchronization of the vertices located in other layer networks is developed with the support of synchronization for the pinned vertices. Employing Lyapunov method, graph theory and stochastic analysis technique, a criterion of almost sure global exponential synchronization is obtained. By adopting the concepts of average noise control rate and average noise control period proposed recently, we lessen the conservativeness of the conditions restricted on aperiodically intermittent noise control to optimize our results. Furthermore, an application to a class of Chua’s circuits is exhibited in detail. In the end, we provide a numerical example to verify the validity of the theoretical results.

中文翻译:

通过间歇性钉扎噪声几乎确定的多层网络同步:基于白噪声的时变耦合

本文关注的是一个多层网络的几乎确定的指数同步,该网络建立在一个非强连接有向图上,该有向图可以通过 Tarjan 算法分为多个层。注意,在多层网络中,提出了基于白噪声的时变耦合和漂移项耦合来模拟顶点之间两种共存的可区分交互。我们开发了一个正常的分析框架来研究多层网络的同步。首先,通过不定期的间歇性钉扎噪声,在分层网络中实现了位于第一层的顶点的同步。其次,在扩散项中基于白噪声的时变耦合的影响下,位于其他层网络中的顶点的同步是在固定顶点的同步支持下开发的。利用李雅普诺夫方法、图论和随机分析技术,得到了几乎肯定全局指数同步的判据。通过采用最近提出的平均噪声控制率和平均噪声控制周期的概念,我们降低了限制非周期性间歇噪声控制条件的保守性,以优化我们的结果。此外,详细展示了对一类蔡氏电路的应用。最后,我们提供了一个数值例子来验证理论结果的有效性。获得了几乎确定全局指数同步的准则。通过采用最近提出的平均噪声控制率和平均噪声控制周期的概念,我们降低了限制非周期性间歇噪声控制条件的保守性,以优化我们的结果。此外,详细展示了对一类蔡氏电路的应用。最后,我们提供了一个数值例子来验证理论结果的有效性。获得了几乎确定全局指数同步的准则。通过采用最近提出的平均噪声控制率和平均噪声控制周期的概念,我们降低了限制非周期性间歇噪声控制条件的保守性,以优化我们的结果。此外,详细展示了对一类蔡氏电路的应用。最后,我们提供了一个数值例子来验证理论结果的有效性。
更新日期:2021-07-13
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