This paper discusses the robustness of neutral-type Cohen-Grossberg neural networks with time delays and stochastic disturbances. And the problem is whether the Cohen-Grossberg neural networks, which originally maintain exponential stability, still achieves exponential stability when subjected to three simultaneous disturbances, namely, time delays, stochastic perturbations, and neutral terms. First, the width of the time delays, the strength of the stochastic disturbances, and the neutral term preset parameter size are derived through the Bellman-Gronwall Lemma, the Itô formula, and the properties of integrals. Next, the values of the three perturbation factors of time delay, stochastic disturbance, and neutral term are obtained by solving a multivariate privacy transcendental equation, which allows the Cohen-Grossberg neural networks to remain exponentially stable after being disturbed. Finally, the numerical example is provided to validate the results of this brief.
Citation: Yijia Zhang, Tao Xie, Yunlong Ma. Robustness analysis of exponential stability of Cohen-Grossberg neural network with neutral terms[J]. AIMS Mathematics, 2025, 10(3): 4938-4954. doi: 10.3934/math.2025226
This paper discusses the robustness of neutral-type Cohen-Grossberg neural networks with time delays and stochastic disturbances. And the problem is whether the Cohen-Grossberg neural networks, which originally maintain exponential stability, still achieves exponential stability when subjected to three simultaneous disturbances, namely, time delays, stochastic perturbations, and neutral terms. First, the width of the time delays, the strength of the stochastic disturbances, and the neutral term preset parameter size are derived through the Bellman-Gronwall Lemma, the Itô formula, and the properties of integrals. Next, the values of the three perturbation factors of time delay, stochastic disturbance, and neutral term are obtained by solving a multivariate privacy transcendental equation, which allows the Cohen-Grossberg neural networks to remain exponentially stable after being disturbed. Finally, the numerical example is provided to validate the results of this brief.
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Yijia Zhang, Tao Xie, Yunlong Ma. Robustness analysis of exponential stability of Cohen-Grossberg neural network with neutral terms[J]. AIMS Mathematics, 2025, 10(3): 4938-4954. doi: 10.3934/math.2025226
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