Periodic solutions of stochastic delay differential equations and applications to logistic equation and neural networks
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In this paper, we consider a class of periodic Ito stochasticdelay differential equations by using the properties of periodic Markovprocesses, and some sufficient conditions for the existence of periodic so-lution of the delay equations are given. These existence theorems improvethe results obtained by Ito et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodicstochastic logistic equation and periodic stochastic neural networks withinfinite delays, respectively. The theorem for the existence of periodic so-lution of periodic stochastic logistic equation improve the result obtainedby Jiang et al. [7].
Abstract
In this paper, we consider a class of periodic Ito stochasticdelay differential equations by using the properties of periodic Markovprocesses, and some sufficient conditions for the existence of periodic so-lution of the delay equations are given. These existence theorems improvethe results obtained by Ito et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodicstochastic logistic equation and periodic stochastic neural networks withinfinite delays, respectively. The theorem for the existence of periodic so-lution of periodic stochastic logistic equation improve the result obtainedby Jiang et al. [7].
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