From networks of unstable attractors to heteroclinic switching

被引：20

作者：

Kirst, Christoph ^{[1
,2
,3
,4
]}

Timme, Marc ^{[1
,2
]}

机构：

[1] Max Planck Inst Dynam & Self Org MPIDS, Network Dynam Grp, D-37073 Gottingen, Germany

[2] BCCN, D-37073 Gottingen, Germany

[3] Univ Gottingen, Fak Phys, D-3400 Gottingen, Germany

[4] Univ Cambridge, Ctr Math Sci, DAMTP, Cambridge CB3 0WA, England

来源：

PHYSICAL REVIEW E | 2008年 / 78卷 / 06期

关键词：

D O I：

10.1103/PhysRevE.78.065201

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other's basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems.

引用

页数：4

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