Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type

被引：22

作者：

Zhou, Douglas ^{[1
]}

Sun, Yi ^{[1
]}

Rangan, Aaditya V. ^{[1
]}

Cai, David ^{[1
,2
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL NEUROSCIENCE | 2010年 / 28卷 / 02期

基金：

美国国家科学基金会;

关键词：

Lyapunov exponents; Non-smooth; Integrate-and-fire; Firing-reset; Refractory-induced degeneracy; INTERSPIKE INTERVAL CORRELATIONS; CORTICAL-NEURONS; ORIENTATION SELECTIVITY; VISUAL-CORTEX; NETWORK MODEL; THRESHOLD; INPUT; CAT; SYNCHRONIZATION; MOTION;

D O I：

10.1007/s10827-009-0201-3

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.

引用

页码：229 / 245

页数：17

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