Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses

Tengda Wei; Xiang Xie; Xiaodi Li; Tengda Wei; Xiang Xie; Xiaodi Li

doi:10.3934/math.2021342

AIMS Mathematics

2021, Volume 6, Issue 6: 5786-5800. doi: 10.3934/math.2021342

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Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses

1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2.
Center for Control and Engineering Computation, Shandong Normal University, Jinan 250014, China

Received: 10 December 2020 Accepted: 22 March 2021 Published: 26 March 2021
MSC : 34K20, 34K45, 35R12

This paper concerns the input-to-state stability problem of delayed reaction-diffusion neural networks with multiple impulses. After reformulating the neural-network model in term of an abstract impulsive functional differential equation, the criteria of input-to-state stability are established by the direct estimate of mild solution and an integral inequality with infinite distributed delay. It shows that the input-to-state stability of the continuous dynamics can be retained under certain multiple impulsive disturbance and the unstable continuous dynamics can be stabilised by the multiple impulsive control, if the intervals between the multiple impulses are bounded. The numerical simulation of two examples is given to show the effectiveness of theoretical results.
- input-to-state stability,
- multiple impulses,
- reaction-diffusion,
- delayed neural networks
Citation: Tengda Wei, Xiang Xie, Xiaodi Li. Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses[J]. AIMS Mathematics, 2021, 6(6): 5786-5800. doi: 10.3934/math.2021342

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Abstract

This paper concerns the input-to-state stability problem of delayed reaction-diffusion neural networks with multiple impulses. After reformulating the neural-network model in term of an abstract impulsive functional differential equation, the criteria of input-to-state stability are established by the direct estimate of mild solution and an integral inequality with infinite distributed delay. It shows that the input-to-state stability of the continuous dynamics can be retained under certain multiple impulsive disturbance and the unstable continuous dynamics can be stabilised by the multiple impulsive control, if the intervals between the multiple impulses are bounded. The numerical simulation of two examples is given to show the effectiveness of theoretical results.

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