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Research Article | Open Access

An analysis of two degenerate double-Hopf bifurcations

Gheorghe Moza1, Mihaela Sterpu2, Carmen Rocşoreanu3( )
Department of Mathematics, Politehnica University of Timisoara, Romania
Department of Mathematics, University of Craiova, Romania
Department of Statistics and Economic Informatics, University of Craiova, Romania
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Abstract

The generic double-Hopf bifurcation is presented in detail in literature in textbooks like references. In this paper we complete the study of the double-Hopf bifurcation with two degenerate (or nongeneric) cases. In each case one of the generic conditions is not satisfied. The normal form and the corresponding bifurcation diagrams in each case are obtained. New possibilities of behavior which do not appear in the generic case were found.

Keywords

double Hopf bifurcationdegenerate double Hopf bifurcationasymptotic analysisbifurcation diagramsnormal forms

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 382-403
DOI: 10.3934/era.2022020

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Cite this article:
Moza G, Sterpu M, Rocşoreanu C. An analysis of two degenerate double-Hopf bifurcations. Electronic Research Archive, 2022, 30(1): 382-403. https://doi.org/10.3934/era.2022020

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Received: 28 October 2021
Revised: 18 December 2021
Accepted: 04 January 2022
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)