Abstract
In this paper, the effects of multiplicative and additive fading stochastic perturbations on the solutions of stochastic difference equations are studied, in which the strength of fading stochastic perturbations is square summable. Different from the existing research, this paper mainly studies the influence of two kinds of stochastic perturbations on the stability of the system, and applies the Lyapunov functional method, the asymptotic mean square trivial sufficiency conditions are obtained for the solutions of stochastic difference equations which based on the influence of multiplicative and additive fading noises. At the same time, the conditions of stochastic perturbation fading rate are obtained. Finally, the above conditions are verified by numerical simulation examples, and the results of numerical simulation show that: (1) the additive perturbations have less influence on the system than the multiplicative perturbations; (2) the fading stochastic perturbations can make the system reach a stable state in a faster time.
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