There are many papers related to stability, some on suppression or on stabilization are one type of them. Functional differential systems are common and important in practice. They are special situations of neutral differential systems and generalization of ordinary differential systems. We discussed conditions on suppression on functional system with Markovian switching in our previous work: “Suppression of Functional System with Markovian Switching”. Based on it, by slightly modifying and adding some conditions, we get this paper. In this paper, we will study a functional system whose coefficient satisfies the local Lipschitz condition and the one-sided polynomial growth condition under Markovian switching. By introducing two appropriate intensity Brownian noise, we find the potential explosion system stabilized.
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