In this paper, based on Razumikhin method, stability of stochastic Lévy noise coupled systems with mixed delays (SLCSD) is researched. Here, both mixed delays and Lévy noise are considered into coupled systems for the first time. Then, by combining Razumikhin method with Lyapunov method and graph theory, several stability criteria including the Razumikhin-type theorem, the Lyapunov-type theorem and a coefficients-type theorem are given to ensure the pth moment exponential stability of SLCSD. In particular, the stability of a class of coupled oscillators and the stability of single-link robot arms are investigated as practical applications of the obtained results. And some numerical simulations are offered to illustrate the feasibility of the obtained results.

本文基于Razumikhin方法，研究了具有混合延迟的随机Lévy噪声耦合系统(SLCSD)的稳定性。在这里，混合延迟和 Lévy 噪声首次被考虑到耦合系统中。然后，将Razumikhin方法与Lyapunov方法和图论相结合，给出了Razumikhin型定理、Lyapunov型定理和系数型定理等几个稳定性判据，以保证SLCSD的p阶矩指数稳定性。特别地，研究了一类耦合振荡器的稳定性和单连杆机械臂的稳定性，作为所得结果的实际应用。并提供了一些数值模拟来说明所得结果的可行性。