Abstract Delay coupled systems have received a great deal of attention in recent years. However, delay coupled systems with hybrid switching diffusions (DCSHSD) have rarely been discussed and are still important. Thus, this paper is devoted to studying the stability of DCSHSD based on Razumikhin method. Then, combining Lyapunov method with graph theory, p th moment exponential stability of DCSHSD is studied and three kinds of stability criteria, including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem, are obtained. Wherein, an upper bound of Lyapunov exponent is estimated. In particular, as a practical application of our theoretical results, stability of delay coupled oscillators with hybrid switching diffusions is studied. Finally, a numerical example is provided to demonstrate the validity and feasibility of the theoretical results.

中文翻译：

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具有混合开关扩散的延迟耦合系统稳定性的 Razumikhin 方法

摘要 时滞耦合系统近年来受到了广泛的关注。然而，具有混合开关扩散（DCSHSD）的延迟耦合系统很少被讨论并且仍然很重要。因此，本文致力于研究基于 Razumikhin 方法的 DCSHSD 的稳定性。然后，将Lyapunov方法与图论相结合，研究了DCSHSD的p阶矩指数稳定性，得到了Razumikhin型定理、Lyapunov型定理和系数型定理3种稳定性判据。其中，估计了一个李雅普诺夫指数的上界。特别是，作为我们理论结果的实际应用，研究了具有混合开关扩散的延迟耦合振荡器的稳定性。最后，