IEEE Trans Neural Netw Learn Syst. 2015 Aug;26(8):1698-709. doi: 10.1109/TNNLS.2014.2352217. Epub 2014 Sep 9.
In this paper, a novel class of stochastic coupled systems with Lévy noise on networks (SCSLNNs) is presented. Both white noise and Lévy noise are considered in the networks. By exploiting graph theory and Lyapunov stability theory, criteria ensuring p th moment exponential stability and stability in probability of these SCSLNNs are established, respectively. These principles are closely related to the topology of the network and the perturbation intensity of white noise and Lévy noise. Moreover, to verify the theoretical results, stochastic coupled oscillators with Lévy noise on a network and stochastic Volterra predator-prey system with Lévy noise are performed. Finally, a numerical example about oscillators' network is provided to illustrate the feasibility of our analytical results.
本文提出了一类具有网络上 Lévy 噪声的新型随机耦合系统（SCSLNNs）。网络中同时考虑了白噪声和 Lévy 噪声。利用图论和 Lyapunov 稳定性理论，分别建立了保证这些 SCSLNNs 的 p 阶矩指数稳定性和概率稳定性的准则。这些原理与网络的拓扑结构以及白噪声和 Lévy 噪声的干扰强度密切相关。此外，为了验证理论结果，在网络上对具有 Lévy 噪声的随机耦合振荡器和具有 Lévy 噪声的随机 Volterra 捕食者-被捕食系统进行了仿真。最后，通过一个关于振荡器网络的数值例子来说明我们分析结果的可行性。
