School of Mathematics and Statistics, Central South University, Changsha, China.
City College, Kunming University of Science and Technology, Kunming, China.
PLoS One. 2019 Aug 7;14(8):e0220861. doi: 10.1371/journal.pone.0220861. eCollection 2019.
By using the semi-discretization technique of differential equations, the discrete analogue of a kind of cellular neural networks with stochastic perturbations and fuzzy operations is formulated, which gives a more accurate characterization for continuous-time models than that by Euler scheme. Firstly, the existence of at least one p-th mean almost periodic sequence solution of the semi-discrete stochastic models with almost periodic coefficients is investigated by using Minkowski inequality, Hölder inequality and Krasnoselskii's fixed point theorem. Secondly, the p-th moment global exponential stability of the semi-discrete stochastic models is also studied by using some analytical skills and the proof of contradiction. Finally, a problem of stochastic stabilization for discrete cellular neural networks is studied.
利用微分方程的半离散化技术，对具有随机扰动和模糊运算的一类细胞神经网络的离散模拟进行了公式化处理，这比欧拉方案更能准确地描述连续时间模型。首先，利用 Minkowski 不等式、Holder 不等式和 Krasnoselskii 不动点定理，研究了具有几乎周期系数的半离散随机模型至少存在一个 p 阶平均几乎周期序列解的存在性。其次，利用一些分析技巧和反证法研究了半离散随机模型的 p 阶矩全局指数稳定性。最后，研究了离散细胞神经网络的随机镇定问题。
