尖峰神经元网络的程度匹配性

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2020-04-01 DOI:10.3934/jcd.2020016

Christian Blasche, S. Means, C. Laing

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引用次数: 6

摘要

度匹配性指的是相对于偶然的预期，两个神经元连接的概率根据它们的进出度而增加或减少。我们研究了在theta神经元网络中这种协调性的影响。Ott/Antonsen ansatz用于推导每个神经元预期状态的方程，然后这些方程在度空间中是粗粒度的。我们生成由配度系数参数化的有效连通性矩阵族，并利用这些矩阵族的SVD分解对粗粒度方程进行有效的数值分岔分析。我们发现，在四种可能的程度选型中，有两种对网络动态没有影响，而另外两种对网络动态有显著影响。

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Degree assortativity in networks of spiking neurons

Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in- or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network of theta neurons. The Ott/Antonsen ansatz is used to derive equations for the expected state of each neuron, and these equations are then coarse-grained in degree space. We generate families of effective connectivity matrices parametrised by assortativity coefficient and use SVD decompositions of these to efficiently perform numerical bifurcation analysis of the coarse-grained equations. We find that of the four possible types of degree assortativity, two have no effect on the networks' dynamics, while the other two can have a significant effect.

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.