The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

Juan Castillo; Jaume Llibre; Fernando Verduzco

doi:https://doi.org/10.1007/s11071-017-3766-9

The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

Juan Castillo, Jaume Llibre, Fernando Verduzco

Department of Mathematics

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

25 Citations (Scopus)

Abstract

© 2017, Springer Science+Business Media B.V. The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.

Original language	English
Pages (from-to)	1829-1840
Journal	Nonlinear Dynamics
Volume	90
Issue number	3
DOIs	https://doi.org/10.1007/s11071-017-3766-9
Publication status	Published - 1 Nov 2017

Keywords

Discontinuous piecewise linear differential systems
Pseudo-Hopf bifurcation
Sliding segment
Unfolding

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https://doi.org/10.1007/s11071-017-3766-9

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title = "The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems",

abstract = "{\textcopyright} 2017, Springer Science+Business Media B.V. The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.",

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AU - Castillo, Juan

AU - Llibre, Jaume

AU - Verduzco, Fernando

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Y1 - 2017/11/1

N2 - © 2017, Springer Science+Business Media B.V. The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.

AB - © 2017, Springer Science+Business Media B.V. The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.

KW - Discontinuous piecewise linear differential systems

KW - Pseudo-Hopf bifurcation

KW - Sliding segment

KW - Unfolding

U2 - https://doi.org/10.1007/s11071-017-3766-9

DO - https://doi.org/10.1007/s11071-017-3766-9

M3 - Article

VL - 90

SP - 1829

EP - 1840

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

ER -

The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

Abstract

Keywords

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