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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. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlinear fractional-order Lasota-Wazewska model with infinite delays. Firstly, we introduce some definitions, lemmas of fraction-order differential equation and a number of properties of Mittag-Leffler function. Then, based on these prepared knowledge and by applying the comparison theorem of fractional-order differential equation and the relationship between characteristic equation of Laplace transform and stability, we prove the permanence, asymptotic stability and asymptotic periodicity of fractional-order Lasota-Wazewska model. After that, we introduce an example to illustrate the main results. [ABSTRACT FROM AUTHOR]