Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations

Renato Huzak

doi:10.3934/dcds.2016.36.171

Article Contents

2016, Volume 36, Issue 1: 171-215. Doi: 10.3934/dcds.2016.36.171

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Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations

Renato Huzak^1,

1.
Hasselt University, Campus Diepenbeek, Agoralaan Gebouw D, 3590 Diepenbeek

Received: June 30, 2014

Revised: August 31, 2014

Published: May 2017

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Abstract

This paper is the continuation of our previous papers [16] and [17] where we studied small-amplitude limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations. We find optimal upper bounds for the number of small-amplitude limit cycles in these slow-fast codimension 3 bifurcations. We use techniques from geometric singular perturbation theory.

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Mathematics Subject Classification: Primary: 34E15, 37G15, 34E20, 34C23, 34C26.

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References

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