Dynamics in the 1:2 spatial resonance with broken reflection symmetry
type: Item
instance of: scholarly article
title: Dynamics in the 1:2 spatial resonance with broken reflection symmetry
zbMATH Open document ID: 1082.37054
published in: Physica D
publication date: 2005-05-12T00:00:00Z
review text: This paper is devoted to the study of effects of small symmetry-breaking perturbations on dynamics near heteroclinic cycles. The authors consider generic effects of breaking \(O(2)\) symmetry down to \(SO(2)\). They show that new types of dynamics are introduced into the system above and beyond the quasiperiodic orbit. Specifically, the authors find secondary Takens-Bogdanov bifurcations, so-called \(T\)-points, and degenerate heteroclinic cycles are responsible for the appearance of new types of global bifurcations, and with them of complex dynamics. Moreover, possible scenarios with increasing symmetry breaking are described.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C28
zbMATH DE Number: 2167904
zbMATH Keywords: Symmetry-breaking
zbMATH Keywords: Mode interaction
zbMATH Keywords: Global bifurcations
zbMATH Keywords: Heteroclinic cycles
author: J. Porter
author: Edgar Knobloch
describes a project that uses: XPPAUT
MaRDI profile type: Publication
full work available at URL: j.physd.2005.01.001
OpenAlex ID: W2026369491
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DOI: 10.1016/J.PHYSD.2005.01.001
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description: scientific article; zbMATH DE number 2167904