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Generalized Transversality, Exchange of Stability and Hopf Bifurcation

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Generalized Transversality, Exchange of Stability and Hopf Bifurcation

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dc.contributor.author Bernfeld, Stephen R. en
dc.date.accessioned 2010-06-09T15:05:54Z en
dc.date.available 2010-06-09T15:05:54Z en
dc.date.issued 1981-02 en
dc.identifier.uri http://hdl.handle.net/10106/2425 en
dc.description.abstract In Hopf bifurcation theory often an exchange of stability of an equilibrium gives rise to the creation of periodic orbits for a one parameter family of differential equations. In particular, let us consider the system in Rn given by [see pdf for notation] where µ E [0,^) for µ sufficiently small, a(µ), ß(µ) and Aµ are C°° in µ with a(0) = 0 and ß(0) = 1. Assume [see pdf for notation] where [see pdf for notation] and for each µ, X, Y, Z are of order greater than one at the origin. Finally, the eigenvalues [see pdf for notation] of the (n-2) x (n-2) matrix A0 satisfy the non-resonance condition [see pdf for notation]. We shall refer to the right hand sides of (10) and (1µ) as f0(x,y,z) and fµ (x,y,z) respectively. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;148 en
dc.subject Hopf bifurcation en
dc.subject Stability properties en
dc.subject Bifurcating periodic orbits en
dc.subject Rn en
dc.subject.lcsh Mathematics Research en
dc.subject.lcsh Differential equations en
dc.title Generalized Transversality, Exchange of Stability and Hopf Bifurcation en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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