Synchronized stationary distribution for stochastic multi-links systems with Markov jump

This paper is concerned with the existence of a synchronized stationary distribution for stochastic multi-links systems with Markov jump (SMMJs). By employing Lyapunov method, Kirchhoff's Matrix Tree Theorem in graph theory as well as M-matrix method, several criteria are given to guarantee the existence of a synchronized stationary distribution of SMMJs, including the Lyapunov-type theorem and a coefficients-type theorem. As a subsequent, the theoretical results are applied to a class of stochastic Markov jump oscillators with multi-links and stochastic multi-links Chua's circuits with Markov jump, which indicates the results present widely applied prospect in various physical systems. Eventually, two examples together with numerical simulations are provided to validate the effectiveness of the theoretical results. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper discusses the existence of synchronized stationary distribution for stochastic multi-links systems with Markov jump. Several criteria are provided to ensure the existence of such distribution, and the theoretical results are applied to stochastic systems such as oscillators and circuits. Examples and numerical simulations are presented to validate the effectiveness of the theoretical results.