Abstract
This paper aims to investigate the stability of random coupled systems on networks with Markovian switching (RCSNM), which is driven by general noise instead of white noise. By using Lyapunov method, graph-theoretical technique as well as stochastic analysis technique, some novel sufficient criteria are derived to ensure the global asymptotical stability in probability and exponential stability in pth moment for RCSNM, respectively. It is worth noting that the two kinds of stability for RCSNM are studied for the first time. Based on the theoretical results, the stability of a class of coupled oscillators with Markovian switching and general noise is investigated. Numerical simulations are also included to show the effectiveness and feasibility of the derived results.
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