Open AccessAn analysis of two degenerate double-Hopf bifurcations
Author(s) -
Gheorghe Tigan,
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Mihaela Sterpu,
Carmen Rocşoreanu,
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Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022020
Subject(s) - degenerate energy levels , hopf bifurcation , bifurcation diagram , mathematics , pitchfork bifurcation , bogdanov–takens bifurcation , bifurcation , saddle node bifurcation , pure mathematics , mathematical analysis , physics , nonlinear system , quantum mechanics
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.