An analysis of two degenerate double-Hopf bifurcations

Gheorghe Moza; Mihaela Sterpu; Carmen Rocşoreanu; Gheorghe Moza; Mihaela Sterpu; Carmen Rocşoreanu

doi:10.3934/era.2022020

Electronic Research Archive

2022, Volume 30, Issue 1: 382-403. doi: 10.3934/era.2022020

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Research article

An analysis of two degenerate double-Hopf bifurcations

1.
Department of Mathematics, Politehnica University of Timisoara, Romania
2.
Department of Mathematics, University of Craiova, Romania
3.
Department of Statistics and Economic Informatics, University of Craiova, Romania

Academic Editor: Enrique Ponce

Received: 28 October 2021 Revised: 18 December 2021 Accepted: 04 January 2022 Published: 13 January 2022

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.
- double Hopf bifurcation,
- degenerate double Hopf bifurcation,
- asymptotic analysis,
- bifurcation diagrams,
- normal forms
Citation: Gheorghe Moza, Mihaela Sterpu, Carmen Rocşoreanu. An analysis of two degenerate double-Hopf bifurcations[J]. Electronic Research Archive, 2022, 30(1): 382-403. doi: 10.3934/era.2022020

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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.

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