Stability analysis of stochastic coupled systems on networks without strong connectedness via hierarchical approach

In this paper, the issues pertaining with the networks without strong connectedness (NWSC) and a class of stochastic coupled systems on them are considered in totality. Towards NWSC, a hierarchical approach is proposed explicitly based on the topological structure of networks, and we also provide some examples to demonstrate the practical applicability of this approach. In addition, through employing the theory of asymptotically autonomous systems along with the Lyapunov method and Kirchhoff׳s matrix tree theorem in graph theory, several sufficient conditions to guarantee the moment exponential stability of stochastic coupled systems on NWSC are presented in the form of Lyapunov-type theorem and coefficients-type criterion. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators on NWSC with sufficient conditions given to determine their stability. Ultimately, a numerical example is provided that lends insight to certifying the effectiveness and feasibility of our theoretical results.