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Attractivity AMP Hopf Bifurcation

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Attractivity AMP Hopf Bifurcation

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dc.contributor.author Salvadori, L. en
dc.contributor.author Negrini, P. en
dc.date.accessioned 2010-06-09T14:53:32Z en
dc.date.available 2010-06-09T14:53:32Z en
dc.date.issued 1978-02 en
dc.identifier.uri http://hdl.handle.net/10106/2421 en
dc.description.abstract Consider the one-parameter family of differential equations [see pdf for notation] where [see pdf for notation] and [see pdf for notation]. Here [see pdf for notation] and [see pdf for notation]. Denoting by [see pdf for notation] the eigenvalues of [see pdf for notation] we shall suppose throughout the paper that [see pdf for notation] and [see pdf for notation]. We are concerned with the general problem of asymptotic stability of the periodic orbits arising in the Hopf bifurcation for (1.1). Such property is related to the asymptotic behaviour of the flow relative to 0 (the critical value of the parameter) near the origin [see pdf for notation] of [see pdf for notation]. Actually the bifurcating periodic orbits are found to be attracting under the general assumption that [see pdf for notation] is asymptotically stable for [see pdf for notation], and there exists an odd integer [see pdf for notation] such that the above character of [see pdf for notation] is recognizable in a suitable sense by the terms of [see pdf for notation] of degree [see pdf for notation] (h-asymptotic stability). Denoting this property by [see pdf for notation], we point out some relevant aspect of our analysis: en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;74 en
dc.subject Asymptotic stability en
dc.subject Hopf bifurcation en
dc.subject.lcsh Differential equations en
dc.subject.lcsh Mathematics Research en
dc.title Attractivity AMP Hopf Bifurcation en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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