Dynamics of one-dimensional spiking neuron models
Dynamics of one-dimensional spiking neuron models
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DOI：
10.1007/s00285-003-0223-9
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发表时间：
2004-01-01
影响因子：
1.9
通讯作者：
Brette, R
中科院分区：
文献类型：
--
作者：
Brette, R
在本文中，我们作出了严格的数学分析一维尖峰神经元模型在一个统一的框架。我们发现，特别是由周期性和非周期性驱动的漏积分器以及它的一些变种满足的条件下，尖峰映射是增加其范围内，没有留下任何空间的混沌行为。导出了李雅普诺夫指数的严格表达式。最后，我们分析了周期性驱动的完美积分器，并表明其范围的相位图的限制总是共轭旋转，我们提供了一个明确的表达的不变测度。
In this paper we make a rigorous mathematical analysis of one-dimensional spiking neuron models in a unified framework. We find that, under conditions satisfied in particular by the periodically and aperiodically driven leaky integrator as well as some of its variants, the spike map is increasing on its range, which leaves no room for chaotic behavior. A rigorous expression of the Lyapunov exponent is derived. Finally, we analyse the periodically driven perfect integrator and show that the restriction of the phase map to its range is always conjugated to a rotation, and we provide an explicit expression of the invariant measure.