论一般连接强度下 NNLIF 神经元模型的渐近行为

IF 2.2 1区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL
María J. Cáceres, José A. Cañizo, Alejandro Ramos-Lora
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引用次数: 0

摘要

我们证明了非线性积分-火神经元模型的渐近行为的新结果。其中,我们给出了不受连通性参数限制的平衡态线性化稳定或不稳定的判据,从而证明了平衡态在某些情况下是稳定或不稳定的。在所有情况下,该准则都可以通过数值检查,使我们能够根据连通性参数b和传输延迟d给出稳定和不稳定平衡点的全貌。我们还给出了相关线性方程的进一步谱结果,并使用它们给出了弱连通性平衡点的非线性稳定性的改进结果,以及线性化和非线性稳定性之间的联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Asymptotic Behavior of the NNLIF Neuron Model for General Connectivity Strength

We prove new results on the asymptotic behavior of the nonlinear integrate-and-fire neuron model. Among them, we give a criterion for the linearized stability or instability of equilibria, without restriction on the connectivity parameter, which provides a proof of stability or instability in some cases. In all cases, this criterion can be checked numerically, allowing us to give a full picture of the stable and unstable equilibria depending on the connectivity parameter b and transmission delay d. We also give further spectral results on the associated linear equation, and use them to give improved results on the nonlinear stability of equilibria for weak connectivity, and on the link between linearized and nonlinear stability.

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来源期刊
Communications in Mathematical Physics
Communications in Mathematical Physics 物理-物理:数学物理
CiteScore
4.70
自引率
8.30%
发文量
226
审稿时长
3-6 weeks
期刊介绍: The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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