Abstract
In the case of a generalized Hopf bifurcation several periodic solutions may branch off from the equilibrium. An elementary procedure is presented for establishing all those bifurcating solutions, as well as their stability behaviour, provided a certain non-degeneracy condition is satisfied.
Zusammenfassung
Im Falle einer verallgemeinerten Hopf-Verzweigung können mehrere periodische Lösungen von der Gleichgewichtslage abzweigen. Es wird ein elementares Verfahren vorgestellt, welches erlaubt, unter einer gewissen Nichtentartungsbedingung diese kleinen periodischen Lösungen sowie ihre Stabilität zu bestimmen.
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Spirig, F. An elementary approach to a generalized Hopf bifurcation. Z. angew. Math. Phys. 44, 1068–1078 (1993). https://doi.org/10.1007/BF00942765
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DOI: https://doi.org/10.1007/BF00942765