Abstract
ABSTRACTIn the previous work by Wu et al., it was shown that the polynomial Brownian noise may suppress the potential explosion of the nonlinear system without the linear growth condition or the one-sided linear growth condition and the linear Brownian noise may stabilise this suppressed system. This paper is a continuation of our previous article and considers the asymptotic properties of the suppressed functional differential system under regime switching. These asymptotic properties show that the suppressed functional differential system by polynomial Brownian noise will grow with at most polynomial speed.
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