Using Lin's method to solve Bykov's problems
type: Item
instance of: scholarly article
title: Using Lin's method to solve Bykov's problems
zbMATH Open document ID: 1312.34083
author: Jürgen Knobloch
author: J. S. W. Lamb
author: Kevin N. Webster
published in: Journal of Differential Equations
publication date: 2014-08-20T00:00:00Z
review text: The authors extend the study of the dynamics near T-point heteroclinic cycles from 3-dimensional space, as previously investigated by Bykov, to higher dimensional space. By considering the existence of `piecewise continuous orbits' called Lin orbits, they employ a functional analytic approach to derive a set of bifurcation equations whose solutions represented orbits of a nonwandering set. In the analysis, they distinguish between cases with real and complex leading eigenvalues of the equilibria. In particular, they reveal the existence of richer dynamics when one of the leading eigenvalues is complex.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6332810
zbMATH Keywords: heteroclinic cycles
zbMATH Keywords: T-point
zbMATH Keywords: leading eigenvalue
zbMATH Keywords: global bifurcation
reviewed by: Kwok-wai Chung
MaRDI profile type: Publication
full work available at URL: j.jde.2014.06.006
OpenAlex ID: W2080895663
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DOI: 10.1016/J.JDE.2014.06.006
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description: scientific article; zbMATH DE number 6332810