Generalized Hopf Bifurcation and h-Asymptotic stability

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Generalized Hopf Bifurcation and h-Asymptotic stability

Show simple item record Salvadori, L. en Bernfeld, Stephen R. en 2010-06-03T16:11:30Z en 2010-06-03T16:11:30Z en 1979-11 en
dc.identifier.uri en
dc.description.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.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;122 en
dc.subject Hopf Bifurcation en
dc.subject Perturbed systems en
dc.subject Bifurcating periodic orbits en
dc.subject Stability of the equilibrium en
dc.subject.lcsh Mathematics Research en
dc.title Generalized Hopf Bifurcation and h-Asymptotic stability en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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