Impulsive Stochastic BAM Neural Networks on an Invariant Under a Translation Time Scale
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Impulsive Stochastic BAM Neural Networks on an Invariant Under a Translation Time Scale Wanqin Wu1 · Li Yang2
Received: 29 August 2019 / Accepted: 25 January 2020 © Springer Nature B.V. 2020
Abstract Since the definition of p-mean almost periodic functions on time scales occupies a fundamental position in studying p-mean almost periodicity for stochastic neural networks, a concept of p-mean almost periodic functions on an invariant under a translation time scale is introduced for the first time in this paper. As an application, the existence and exponential stability of piecewise mean-square almost periodic solutions for a class of high-order BAM neural networks on time scales is studied by using the contraction mapping principal and differential inequality techniques. Finally, a numerical example is presented to illustrate the feasibility of our main results. Keywords Stochastic BAM neural networks · Mean-square almost periodic solution · Exponential stability · Time scales
1 Introduction In recent years, the study of dynamic equations on time scales ([1]) is attracting considerable attentions due to its extensive applications (see [2–8]). As a leading research field, almost periodic time scales and almost periodic solutions for dynamic systems on time scales have been extensively studied since authors in [9, 10] proposed the concepts of almost periodic time scales and uniformly almost periodic functions on time scales under fuzzy background and changing-periodic time scales. Recently, Wang, Agarwal and O’Regan introduced some This work is supported by Tian Yuan Fund of NSFC (No. 11526180), Yunnan Province Education Department Scientific Research Fund Project (No. 2018JS315, No. 2018JS309).
B L. Yang
[email protected] W. Wu [email protected]
1
Yunnan Minzu University, Kunming, Yunnan 650500, People’s Republic of China
2
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, People’s Republic of China
W. Wu, L. Yang
concepts and established some basic almost periodic theory and its generalizations on time scales (see [11–15]). They provided the definition of relatively dense set on time scales to establish a concept of uniformly almost periodic functions on time scales (see [16]). Based on their work, we can easily observe that it is very necessary and pivotal to introduce a definition of p-mean almost periodic functions on an invariant under a translation time scale and study the prosperities of solutions for stochastic differential equations. On the other hand, in a real neural system, the stability of neural networks could be enhanced or weakened by some stochastic inputs [17]. Therefore, it is significant to consider the dynamics of stochastic neural networks. With respect to stochastic neural networks, there are many works on the stability. For example, in [18–21], the scholars studied the stability of different classes of stochastic neural networks. For other results on stochastic neural networks, the reader may see [22–27] and reference therein. Mor
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