This article investigates the stabilization of stochastic highly non-linear coupled systems (SHNCSs) with multiple time delays by using periodically intermittent control (PIC). It is worth noting that coefficients in SHNCSs dissatisfy the linear growth condition, which weakens the previous stability conditions. In addition, PIC and multiple time delays are first introduced into the study of highly nonlinear systems, which leads to the existing methods being inapplicable to investigate the stability of SHNCSs with multiple time delays. Therefore, a novel Halanay-type differential inequality is established, which can be employed to deal with highly nonlinear systems with PIC. Based on the Lyapunov method, the graph theory, and the novel differential inequality, SHNCSs with multiple time delays are first studied, and stability criteria are presented. Next, the theoretical results can be applied to modified FitzHugh–Nagumo models. At last, a numerical example is presented to show the effectiveness of our results.

中文翻译：

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多时滞随机高度非线性耦合系统稳定的间歇控制


本文通过使用周期性间歇控制 (PIC) 研究了具有多个时滞的随机高度非线性耦合系统 (SHNCS) 的稳定性。值得注意的是，SHNCS 中的系数不满足线性增长条件，这削弱了先前的稳定性条件。此外，PIC和多时滞首次被引入到高度非线性系统的研究中，这导致现有的方法不适用于研究多时滞SHNCS的稳定性。因此，建立了一种新的Halanay型微分不等式，可用于处理带有PIC的高度非线性系统。基于Lyapunov方法、图论和新的微分不等式，首先研究了多时滞SHNCS，并提出了稳定性判据。接下来，理论结果可以应用于修改后的 FitzHugh-Nagumo 模型。最后，给出了一个数值例子来说明我们结果的有效性。