Random periodic oscillations and global mean-square exponential stability of discrete-space and discrete-time stochastic competitive neural networks with Dirichlet boundary condition
Affiliations: [a] Yunnan Tourism College, Kunming, P.R. China | [b] Department of Mathematics, Yunnan University, Kunming, P.R. China | [c] School of Basic Science, Guilin University of Technology at Nanning, Nanning Guangxi, P.R. China
Correspondence:
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Corresponding author. Dong Pan, School of Basic Science, Guilin University of Technology at Nanning, Nanning Guangxi 530001, P.R. China. E-mail: mathsdpan@163.com.
Abstract: The current article explores the affects of space-time discrete stochastic competitive neural networks. In line with a discrete-space and discrete-time constant variation formula, boundedness and stability are addressed to the space-time discrete stochastic competitive neural networks. Notably, the best convergence speed can be computed by a non-linear optimization problem. In the end, random periodic sequences with respect to time variable of the discrete-space and discrete-time stochastic competitive neural networks are discussed. The results indicate that spatial diffusion with non-negative density factors has no effect on the global mean square boundedness and stability and random periodicity of the network model. The current article is precursory in consideration of space-time discrete competitive neural networks.
