Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models

被引：11

作者：

Barrio, R. ^{[1
,2
,3
,4
]}

Lefranc, M. ^{[5
,6
]}

Martinez, M. A. ^{[3
,4
]}

Serrano, S. ^{[1
,2
,3
,4
]}

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, E-50009 Zaragoza, Spain

[2] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

[3] Univ Zaragoza, CODY, E-50009 Zaragoza, Spain

[4] Univ Zaragoza, GME, E-50009 Zaragoza, Spain

[5] CNRS, UMR8523, Lab Phys Lasers Atomes & Mol, F-59655 Villeneuve Dascq, France

[6] Univ Sci & Technol, F-59655 Villeneuve Dascq, France

来源：

EPL | 2015年 / 109卷 / 02期

关键词：

TOPOLOGICAL ANALYSIS; TEMPLATE ANALYSIS; PERIODIC-ORBITS; ATTRACTORS; ENCODINGS; EQUATIONS; LASER;

D O I：

10.1209/0295-5075/109/20002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We characterize the systematic changes in the topological structure of chaotic attractors that occur as spike-adding and homoclinic bifurcations are encountered in the slow-fast dynamics of neuron models. This phenomenon is detailed in the simple Hindmarsh-Rose neuron model, where we show that the unstable periodic orbits appearing after each spike-adding bifurcation are associated with specific symbolic sequences in the canonical symbolic encoding of the dynamics of the system. This allows us to understand how these bifurcations modify the internal structure of the chaotic attractors. Copyright (C) EPLA, 2015

引用

页数：6

共 31 条

[1]

[Anonymous], 2011, The topology of chaos

[2]

Arai Z., 2013, NONLINEAR THEORY ITS, V1, P104

[3] Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons [J].