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Input-to-State Stability for Stochastic Delay Neural Networks with Markovian Switching

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Abstract

In this paper, some problems on the input-to-state stability, integral input-to-state stability, and stochastic input-to-state stability of stochastic non-autonomous neural networks with time-varying delay and Markovian switching are investigated. By using the generalized integral inequality, the Lyapunov function approach and the stochastic analysis theory, the input-to-state stability, integral input-to-state stability, and stochastic input-to-state stability for such neural networks are discussed when the time-varying delay is a bounded function. The integral input-to-state stability and stochastic input-to-state stability are also implied. One example is given to illustrate the derived theoretical result.

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Acknowledgements

The authors are very grateful to the reviewers for their valuable suggestions and comments for improving the quality of this work. This work is partially supported by the National Natural Science Foundation of China under grant number 62163027, and the Natural Science Foundation of Jiangxi Province of China under grant number 20171BCB23001.

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  1. Department of Mathematics, School of Science, Nanchang University, Nanchang, 330031, People’s Republic of China

    Yumei Fan & Huabin Chen

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  1. Yumei Fan
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  2. Huabin Chen
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Correspondence to Huabin Chen.

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Fan, Y., Chen, H. Input-to-State Stability for Stochastic Delay Neural Networks with Markovian Switching. Neural Process Lett 53, 4389–4406 (2021). https://doi.org/10.1007/s11063-021-10605-8

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