The existence of a stationary distribution for stochastic coupled oscillators

This paper addresses a stochastic coupled oscillators model. By employing the Lyapunov function method combined with Kirchhoff’s Matrix Tree Theorem in graph theory, we establish a sufficient criterion to guarantee the existence of a stationary distribution for stochastic coupled oscillators. Moreover, a numerical example is given to illustrate the effectiveness of our theoretical results. •The problem we considered is the existence of a stationary distribution of a stochastic coupled oscillators model.•By using the Lyapunov method and Kirchhoff’s Matrix Tree Theorem.•The approach we employ avoids constructing a Lyapunov function directly .