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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Asymptotic Stability of a Class of Neutral Delay Neuron System in a Critical Case
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Asymptotic Stability of a Class of Neutral Delay Neuron System in a Critical Case

机译：一类中性延迟神经元系统在临界情况下的渐近稳定性

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摘要

In this brief, the asymptotic stability properties of a neutral delay neuron system are studied mainly in a critical case when the exponential stability is not possible. If a critical value of the coefficient in the neutral delay neuron system is considered, then the difficulty for our investigation is caused by the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis. It is obvious that, in such a case, the equation is not exponentially stable, and one needs more subtle methods in order to characterize this type of asymptotic stability. Hence, first, the local asymptotic stability for the neutral delay neuron system is studied, and the main tools involved are the asymptotic expansions of characteristic roots, Laplace transforms, and function series, and a complete analysis of the stability diagram is also presented. Then, based on the energy method, the globally asymptotic stability results for the neutral delay neuron system are derived.
机译：在本文中，主要在无法实现指数稳定性的关键情况下研究中性延迟神经元系统的渐近稳定性。如果考虑中性延迟神经元系统中系数的临界值，则我们的研究困难是由于线性算子的频谱渐近逼近虚轴这一事实引起的。显然，在这种情况下，该方程不是指数稳定的，为了表征这种渐近稳定性，人们需要更多细微的方法。因此，首先，研究中性时滞神经元系统的局部渐近稳定性，其中涉及的主要工具是特征根的渐近展开，Laplace变换和函数系列，并给出了稳定性图的完整分析。然后，基于能量方法，得出了中性时滞神经元系统的全局渐近稳定性结果。

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