Robustness analysis of neutral fuzzy cellular neural networks with stochastic disturbances and time delays

Yunlong Ma; Tao Xie; Yijia Zhang; Yunlong Ma; Tao Xie; Yijia Zhang

doi:10.3934/math.20241431

AIMS Mathematics

2024, Volume 9, Issue 10: 29556-29572. doi: 10.3934/math.20241431

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Theory article

Robustness analysis of neutral fuzzy cellular neural networks with stochastic disturbances and time delays

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

Received: 16 July 2024 Revised: 08 September 2024 Accepted: 29 September 2024 Published: 17 October 2024
MSC : 93B35, 93D23

This paper discusses the robustness of neutral fuzzy cellular neural networks with stochastic disturbances and time delays. This work questions whether fuzzy cellular neural networks, which initially remains stable, can be stabilised again when the system is subjected to three simultasneous perturbations i.e., neutral items, random disturbances, and time delays. First, by using inequality techniques such as Gronwall's Lemma, the Itŏ formula, and the property of integrals, the transcendental equations that contain the contraction coefficient of the neutral terms, the intensity of the random disturbances, and the time delays are derived. Then, the upper bounds of the neutral terms, random disturbances, and time delays are estimated by solving the transcendental equations for multifactor perturbations, which ensures that the disturbed fuzzy cellular neural network can be stabilised again. Finally, the validity of the results is verified by numerical examples.
- fuzzy cellular neural networks,
- neutral terms,
- stochastic disturbances,
- time delays,
- robustness
Citation: Yunlong Ma, Tao Xie, Yijia Zhang. Robustness analysis of neutral fuzzy cellular neural networks with stochastic disturbances and time delays[J]. AIMS Mathematics, 2024, 9(10): 29556-29572. doi: 10.3934/math.20241431

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Abstract

This paper discusses the robustness of neutral fuzzy cellular neural networks with stochastic disturbances and time delays. This work questions whether fuzzy cellular neural networks, which initially remains stable, can be stabilised again when the system is subjected to three simultasneous perturbations i.e., neutral items, random disturbances, and time delays. First, by using inequality techniques such as Gronwall's Lemma, the Itŏ formula, and the property of integrals, the transcendental equations that contain the contraction coefficient of the neutral terms, the intensity of the random disturbances, and the time delays are derived. Then, the upper bounds of the neutral terms, random disturbances, and time delays are estimated by solving the transcendental equations for multifactor perturbations, which ensures that the disturbed fuzzy cellular neural network can be stabilised again. Finally, the validity of the results is verified by numerical examples.

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