Robust heteroclinic cycles
type: Item
instance of: scholarly article
title: Robust heteroclinic cycles
zbMATH Open document ID: 0879.58054
DOI: 10.1007/BF02677976
author: O. Diekmann
published in: Journal of Nonlinear Science
publication date: 1998-01-29T00:00:00Z
review text: A heteroclinic cycle in a dynamical system is given by a finite cyclic sequence of trajectories each connecting two fixed points. Robustness means that a cycle nearby still exists after perturbing the system in a particular admissible way. Here, one allows for a stable state with high symmetry to lose its stability and some of its symmetry. Or the perturbations applied let the system stay within a specified class of systems. Part I describes two typical representatives of the phenomenon. Part II surveys the results known so far on the theoretical side. Part III discusses applications to particular systems appearing as mathematical models in some context.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34-02
zbMATH DE Number: 1016992
zbMATH Keywords: symmetry breaking
zbMATH Keywords: bifurcation
zbMATH Keywords: mathematical model
zbMATH Keywords: stability
reviewed by: Dieter Erle
MaRDI profile type: Publication
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Robust heteroclinic cycles (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02677976

Robust heteroclinic cycles (OpenAlex ID)
OpenAlex ID: W2032150785

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