An analysis of two degenerate double-Hopf bifurcations

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 co...

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Bibliographic Details
Published in:Electronic Research Archive
Main Authors: Gheorghe Moza, Mihaela Sterpu, Carmen Rocşoreanu
Format: Article
Language:English
Published: AIMS Press 2022-01-01
Subjects:
double hopf bifurcation
degenerate double hopf bifurcation
asymptotic analysis
bifurcation diagrams
normal forms
Online Access:https://www.aimspress.com/article/doi/10.3934/era.2022020?viewType=HTML
Description
Summary: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.
ISSN:2688-1594

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