PERIODIC SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS TO LOGISTIC EQUATION AND NEURAL NETWORKS
PERIODIC SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS TO LOGISTIC EQUATION AND NEURAL NETWORKS
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随机时滞微分方程的周期解及其在逻辑方程和神经网络中的应用
DOI：
10.4134/jkms.2013.50.6.1165
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发表时间：
2013-11-01
影响因子：
0.6
通讯作者：
Xu, Daoyi
中科院分区：
文献类型：
--
作者：
Li, Dingshi;Xu, Daoyi
本文利用周期马尔可夫过程的性质考虑一类周期伊藤随机时滞微分方程，并给出了时滞方程周期解存在的一些充分条件。这些存在定理改进了 Ito 等人获得的结果。 [6]，拜诺夫等人。 [1] 和徐等人。 [15]。作为应用，我们分别研究了周期随机Logistic方程和无限时滞周期随机神经网络周期解的存在性。周期随机Logistic方程周期解存在性定理改进了Jiang等人的结果。 [7]。
In this paper, we consider a class of periodic Ito stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the 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 periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].