Construction of codimension one homoclinic cycles

A.J. Homburg; M. Kellner; J. Knobloch

doi:10.1080/14689367.2013.860085

Construction of codimension one homoclinic cycles

A.J. Homburg, M. Kellner, J. Knobloch

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We give an explicit construction of families of Dm-equivariant polynomial vector fields in possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m equal to a multiple of 4, where the bifurcations form an open problem. © 2013 © 2013 Taylor & Francis.

Original language	English
Pages (from-to)	133-151
Journal	Dynamical Systems-an International Journal
Volume	29
Issue number	1
DOIs	https://doi.org/10.1080/14689367.2013.860085
Publication status	Published - 2014

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AU - Kellner, M.

AU - Knobloch, J.

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AB - We give an explicit construction of families of Dm-equivariant polynomial vector fields in possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m equal to a multiple of 4, where the bifurcations form an open problem. © 2013 © 2013 Taylor & Francis.

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DO - 10.1080/14689367.2013.860085

M3 - Article

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VL - 29

SP - 133

EP - 151

JO - Dynamical Systems-an International Journal

JF - Dynamical Systems-an International Journal

IS - 1

ER -

Construction of codimension one homoclinic cycles

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