Pseudo-Hopf Bifurcation for a Class of 3D Filippov Linear Systems

José Manuel Islas; Juan Castillo; Baltazar Aguirre-Hernandez; Fernando Verduzco

doi:10.1142/S0218127421500255

Pseudo-Hopf Bifurcation for a Class of 3D Filippov Linear Systems

José Manuel Islas, Juan Castillo, Baltazar Aguirre-Hernandez, Fernando Verduzco

Departamento de Matemáticas

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

10 Scopus citations

Abstract

We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.

Original language	English
Article number	2150025
Journal	International Journal of Bifurcation and Chaos
Volume	31
Issue number	2
DOIs	https://doi.org/10.1142/S0218127421500255
State	Published - Feb 2021

Bibliographical note

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

Filippov systems
Pseudo-Hopf bifurcation
crossing limit cycle

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10.1142/S0218127421500255

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abstract = "We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.",

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AU - Aguirre-Hernandez, Baltazar

AU - Verduzco, Fernando

PY - 2021/2

Y1 - 2021/2

N2 - We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.

AB - We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.

KW - Filippov systems

KW - Pseudo-Hopf bifurcation

KW - crossing limit cycle

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U2 - 10.1142/S0218127421500255

DO - 10.1142/S0218127421500255

M3 - Artículo

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JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

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M1 - 2150025

ER -

Pseudo-Hopf Bifurcation for a Class of 3D Filippov Linear Systems

Abstract

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Keywords

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