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dc.contributor.authorSalvadori, L.en
dc.contributor.authorBernfeld, Stephen R.en
dc.date.accessioned2010-06-03T16:11:30Zen
dc.date.available2010-06-03T16:11:30Zen
dc.date.issued1979-11en
dc.identifier.urihttp://hdl.handle.net/10106/2299en
dc.description.abstract**Please note that the full text is embargoed** ABSTRACT: The prevalent approach to the Hopf bifurcation problem is to prove directly the existence of the bifurcating periodic orbits by using such standard procedures as the implicit function theorem, the LiapunovSchmidt method and its known variants, and topological degree arguments (see [7]). The phenomenon of Hopf bifurcation often occurs because of exchange of stability properties of the equilibrium under perturbations (see for instance, Chafee in [7] p. 85-88,Andronov et. al. [1], Marchetti et. al. [6] and Negrini and Salvadori [8]). This connection between the exchange of stability of the equilibrium and the appearance of bifurcating periodic orbits can be carefully investigated in order to develop a different approach for obtaining existence results and qualitative properties of these orbits. Now we want to provide a systematic development of the procedure sketched in [6] and [8] by considering the generalized Hopf bifurcation as was studied by Chafee [3] who used the alternative method as described by Hale [4]. In particular consider an n dimensional system of differential equations [see pdf for notation]. Assume the Jacobian matrix if [see pdf for notation] has a complex conjugate pair of eigenvalues ±i and that all other eigenvalues [see pdf for notation].en
dc.language.isoen_USen
dc.publisherUniversity of Texas at Arlingtonen
dc.relation.ispartofseriesTechnical Report;122en
dc.subjectHopf Bifurcationen
dc.subjectPerturbed systemsen
dc.subjectBifurcating periodic orbitsen
dc.subjectStability of the equilibriumen
dc.subject.lcshMathematics Researchen
dc.titleGeneralized Hopf Bifurcation and h-Asymptotic stabilityen
dc.typeTechnical Reporten
dc.publisher.departmentDepartment of Mathematicsen


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