Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields

Jaume Llibre; Enrique Ponce

doi:https://doi.org/10.1016/S0362-546X(98)00175-8

Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields

Jaume Llibre, Enrique Ponce

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

24 Citations (Scopus)

Abstract

An account is given of a bifurcation that represents a form of generalized Hopf bifurcation from the infinity. In particular, the bifurcation of a periodic orbit from infinity for differential systems is explored. Necessary and sufficient conditions for the bifurcation are clarified. The existence, uniqueness, and stability of the bifurcating orbit are detailed. Furthermore, an asymptotic estimate for the size of the orbit is obtained.

Original language	English
Pages (from-to)	623-653
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	36
DOIs	https://doi.org/10.1016/S0362-546X(98)00175-8
Publication status	Published - 1 Jun 1999

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title = "Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields",

abstract = "An account is given of a bifurcation that represents a form of generalized Hopf bifurcation from the infinity. In particular, the bifurcation of a periodic orbit from infinity for differential systems is explored. Necessary and sufficient conditions for the bifurcation are clarified. The existence, uniqueness, and stability of the bifurcating orbit are detailed. Furthermore, an asymptotic estimate for the size of the orbit is obtained.",

author = "Jaume Llibre and Enrique Ponce",

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AU - Llibre, Jaume

AU - Ponce, Enrique

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Y1 - 1999/6/1

N2 - An account is given of a bifurcation that represents a form of generalized Hopf bifurcation from the infinity. In particular, the bifurcation of a periodic orbit from infinity for differential systems is explored. Necessary and sufficient conditions for the bifurcation are clarified. The existence, uniqueness, and stability of the bifurcating orbit are detailed. Furthermore, an asymptotic estimate for the size of the orbit is obtained.

AB - An account is given of a bifurcation that represents a form of generalized Hopf bifurcation from the infinity. In particular, the bifurcation of a periodic orbit from infinity for differential systems is explored. Necessary and sufficient conditions for the bifurcation are clarified. The existence, uniqueness, and stability of the bifurcating orbit are detailed. Furthermore, an asymptotic estimate for the size of the orbit is obtained.

U2 - https://doi.org/10.1016/S0362-546X(98)00175-8

DO - https://doi.org/10.1016/S0362-546X(98)00175-8

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EP - 653

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