2<em>p</em>-th mean dynamic behaviors for semi-discrete stochastic competitive neural networks with time delays

Tianwei Zhang; Zhouhong Li; Jianwen Zhou; Tianwei Zhang; Zhouhong Li; Jianwen Zhou

doi:10.3934/math.2020413

AIMS Mathematics

2020, Volume 5, Issue 6: 6419-6435. doi: 10.3934/math.2020413

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Research article

2p-th mean dynamic behaviors for semi-discrete stochastic competitive neural networks with time delays

1.
Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2.
City College, Kunming University of Science and Technology, Kunming 650051, China
3.
Department of Mathematics, Yuxi Normal University, Yuxi 653100, Yunnan, China

Received: 22 June 2020 Accepted: 11 August 2020 Published: 14 August 2020
MSC : 39A24, 39A30, 39A50, 92B20

In this article, a novel semi-discrete model for stochastic competitive neural networks (SCNNs) is proposed. At first, taking advantage of some famous inequalities and fixed point theory, a few conditions are obtained for the existence of 2p-th mean almost periodic sequence (MAPS) of the semi-discrete stochastic model. In the next palace, 2p-th moment global exponential stability (MGES) of the above model is discussed as well. The research findings exhibit the stochastic and delayed effects on the mean dynamics of the semi-discrete stochastic networks. In the end, some numerical illustrations are presented to visually expound the feasibility of the works in this paper. The methods in this article could be applied to investigate other models in the areas of science and engineering.
- competitive neural networks,
- semi discreteness,
- stochastic process,
- fixed point theory
Citation: Tianwei Zhang, Zhouhong Li, Jianwen Zhou. 2p-th mean dynamic behaviors for semi-discrete stochastic competitive neural networks with time delays[J]. AIMS Mathematics, 2020, 5(6): 6419-6435. doi: 10.3934/math.2020413

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Abstract

In this article, a novel semi-discrete model for stochastic competitive neural networks (SCNNs) is proposed. At first, taking advantage of some famous inequalities and fixed point theory, a few conditions are obtained for the existence of 2p-th mean almost periodic sequence (MAPS) of the semi-discrete stochastic model. In the next palace, 2p-th moment global exponential stability (MGES) of the above model is discussed as well. The research findings exhibit the stochastic and delayed effects on the mean dynamics of the semi-discrete stochastic networks. In the end, some numerical illustrations are presented to visually expound the feasibility of the works in this paper. The methods in this article could be applied to investigate other models in the areas of science and engineering.

References

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