ABSTRACT This paper investigates the stabilisation of stochastic coupled systems with time-varying delays and Lévy noise on networks (SCSTLN) via periodically intermittent control. And here, internal delays, white noise and Lévy noise are considered in the networks. To ensure stability of SCSTLN with a periodically intermittent controller, several simple and useful criteria are obtained by establishing a new differential inequality and using a graph-theoretic approach. The intensity of control is closely related to the coupling strength and the perturbed intensity of white noise and Lévy noise. In particular, the stabilisation of stochastic coupled oscillators with time-varying delays and Lévy noise on a network as a practical application of our theoretical results is studied. Finally, a numerical example about oscillators network is carried out to show the validity and feasibility of our analytical results.

中文翻译：

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通过周期性间歇控制在网络上稳定具有 L$\acute {{\rm e}}$vy 噪声的随机延迟系统

摘要 本文通过周期性间歇控制研究了具有时变延迟和网络上的 Lévy 噪声 (SCSTLN) 的随机耦合系统的稳定性。在这里，网络中考虑了内部延迟、白噪声和 Lévy 噪声。为了确保具有周期性间歇控制器的 SCSTLN 的稳定性，通过建立新的微分不等式并使用图论方法获得了几个简单而有用的标准。控制的强度与白噪声和Lévy噪声的耦合强度和扰动强度密切相关。特别是，作为我们理论结果的实际应用，研究了网络上具有时变延迟和 Lévy 噪声的随机耦合振荡器的稳定性。最后，