Stationary distribution of stochastic Markov jump coupled systems based on graph theory. (February 2019) - Liu, Yan; Yu, Pinrui; Chu, Dianhui; Su, Huan
Highlights: Stationary distribution of Markov jump stochastic coupled systems. A new method of combining graph theory, M-matrix and Lyapunov method to the issue. Applications to Markov jump stochastic coupled oscillator systems. Abstract: This paper focuses on the existence of a stationary distribution of stochastic Markov jump coupled systems (SMJCSs) for the first time, in which the coupling effect is considered. A new technique that is combining the graph theory, M-matrix method with the Lyapunov method is used to study stationary distribution, and sufficient conditions are presented to ensure the existence of a stationary distribution, which are more applicable and suitable for various fields, such as neural networks, biomathematics, physics and so forth. Moreover, sufficient conditions presented indicate that the existing region of stationary distribution is related to stochastic disturbance and the dimension of a system closely. Also, theoretical results are applied to stochastic Markov jump coupled oscillators systems in physics and then a specific theorem is presented. Eventually, some simulations are given to verify the feasibility and availability of our theoretical results.