This paper is concerned with the existence of stationary distribution of stochastic multi-layer networks with Markovian switching (SMLNMS). Fitst, a new complex network model is proposed, that is stochastic coupled system driven by Brownian motion and Markovian switching. White noise, telegraph noise, intra-layer and inter-layer couplings are considered in model. Then, in view of graph theory, M-matrix theory and Lyapunov method, Lyapunov-type and coefficient-type theorems are proposed to probe the existence criteria of stationary distribution of SMLNMS. Finally, a stochastic multi-layer SEIS with Markovian switching is presented as an application to validate the validity of the theoretical results.

中文翻译：

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马尔可夫切换随机多层网络平稳分布存在性的图论方法


本文关注马尔可夫切换随机多层网络（SMLNMS）平稳分布的存在性。 Fitst提出了一种新的复杂网络模型，即布朗运动和马尔可夫切换驱动的随机耦合系统。模型中考虑了白噪声、电报噪声、层内和层间耦合。然后，结合图论、M矩阵理论和Lyapunov方法，提出了Lyapunov型和系数型定理来探讨SMLNMS平稳分布的存在准则。最后，提出了一种具有马尔可夫切换的随机多层 SEIS 作为应用来验证理论结果的有效性。