具有指数时间核的神经场动力学。

IF 1.3 4区 生物学 Q3 BIOLOGY
Theory in Biosciences Pub Date : 2024-06-01 Epub Date: 2024-03-09 DOI:10.1007/s12064-024-00414-7
Elham Shamsara, Marius E Yamakou, Fatihcan M Atay, Jürgen Jost
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引用次数: 0

摘要

我们考虑了具有指数时间核的标准神经场方程。我们分析了平衡解与时间无关的(静态)和与时间有关的(动态)分岔以及新出现的时空波形。我们发现,指数时间内核不允许出现静态分岔,如鞍节点、叉形分岔,特别是静态图灵分岔。然而,指数时间核具有一个重要特性,即它考虑到了神经元对过去活动的有限记忆,而格林函数则没有考虑到这一点。通过动态分岔分析,我们给出了明确的分岔条件。霍普夫分岔会产生时间非恒定但空间恒定的解,而图灵-霍普夫分岔则会产生空间和时间非恒定的解,尤其是行波。分岔参数包括指数时间核的系数、神经信号的传输速度、突触的时延率以及兴奋性与抑制性突触权重之比。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamics of neural fields with exponential temporal kernel.

We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.

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来源期刊
Theory in Biosciences
Theory in Biosciences 生物-生物学
CiteScore
2.70
自引率
9.10%
发文量
21
审稿时长
3 months
期刊介绍: Theory in Biosciences focuses on new concepts in theoretical biology. It also includes analytical and modelling approaches as well as philosophical and historical issues. Central topics are: Artificial Life; Bioinformatics with a focus on novel methods, phenomena, and interpretations; Bioinspired Modeling; Complexity, Robustness, and Resilience; Embodied Cognition; Evolutionary Biology; Evo-Devo; Game Theoretic Modeling; Genetics; History of Biology; Language Evolution; Mathematical Biology; Origin of Life; Philosophy of Biology; Population Biology; Systems Biology; Theoretical Ecology; Theoretical Molecular Biology; Theoretical Neuroscience & Cognition.
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