Robustness analysis of Cohen-Grossberg neural network with piecewise constant argument and stochastic disturbances

Tao Xie; Wenqing Zheng; Tao Xie; Wenqing Zheng

doi:10.3934/math.2024151

AIMS Mathematics

2024, Volume 9, Issue 2: 3097-3125. doi: 10.3934/math.2024151

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Research article

Robustness analysis of Cohen-Grossberg neural network with piecewise constant argument and stochastic disturbances

Tao Xie ^,,
Wenqing Zheng

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, Hubei, China

Received: 15 November 2023 Revised: 15 December 2023 Accepted: 20 December 2023 Published: 02 January 2024
MSC : 34D20

Robustness of neural networks has been a hot topic in recent years. This paper mainly studies the robustness of the global exponential stability of Cohen-Grossberg neural networks with a piecewise constant argument and stochastic disturbances, and discusses the problem of whether the Cohen-Grossberg neural networks can still maintain global exponential stability under the perturbation of the piecewise constant argument and stochastic disturbances. By using stochastic analysis theory and inequality techniques, the interval length of the piecewise constant argument and the upper bound of the noise intensity are derived by solving transcendental equations. In the end, we offer several examples to illustrate the efficacy of the findings.
- Cohen-Grossberg neural network,
- robustness,
- piecewise constant argument,
- stochastic disturbances
Citation: Tao Xie, Wenqing Zheng. Robustness analysis of Cohen-Grossberg neural network with piecewise constant argument and stochastic disturbances[J]. AIMS Mathematics, 2024, 9(2): 3097-3125. doi: 10.3934/math.2024151

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Abstract

Robustness of neural networks has been a hot topic in recent years. This paper mainly studies the robustness of the global exponential stability of Cohen-Grossberg neural networks with a piecewise constant argument and stochastic disturbances, and discusses the problem of whether the Cohen-Grossberg neural networks can still maintain global exponential stability under the perturbation of the piecewise constant argument and stochastic disturbances. By using stochastic analysis theory and inequality techniques, the interval length of the piecewise constant argument and the upper bound of the noise intensity are derived by solving transcendental equations. In the end, we offer several examples to illustrate the efficacy of the findings.

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