Synchronized stationary distribution for stochastic multi-links systems with Markov jump. (May 2021) - Zhao, Xin; Lu, Xijing; Zeng, Zhijun
Abstract: 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. Highlights: The synchronized stationary distribution for stochastic multi-links systems with Markov jump (SMMJs) is studied for the first time in this paper. Based on Lyapunov method, graph theory and some inequality techniques, several criteria are given to guarantee the existence of a synchronized stationary distribution of SMMJs. We study stochastic Markov jump oscillators with multi-links and stochastic multi-links Chua's circuits with Markov jump as practical applications of SMMJs.