Infinitely many multi-pulses near a bifocal cycle

Alexandre A. P. Rodrigues

doi:10.3934/proc.2015.0954

Article Contents

2015, Volume 2015: 954-964. Doi: 10.3934/proc.2015.0954 open access

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Infinitely many multi-pulses near a bifocal cycle

Alexandre A. P. Rodrigues^1,

1.
Centro de Matemática da Universidade do Porto and Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto

Received: July 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

The entire dynamics in a neighbourhood of a reversible heteroclinic cycle involving a bifocus is far from being understood. In this article, using the well known theory of reversing symmetries, we prove that there are infinitely many pulses near a cycle involving two symmetric equilibria, a real saddle and a bifocus, giving rise to a complex network. We also conjecture that suspended blenders might appear in the neighbourhood of the network.

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Mathematics Subject Classification: Primary: 37C29; Secondary: 34C28, 37C27, 37C20.

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References

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