Bifurcations of snap-back repellers with application to border-collision bifurcations

Paul Glendinning

doi:10.1142/S0218127410025557

Bifurcations of snap-back repellers with application to border-collision bifurcations

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Abstract

The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations. © 2010 World Scientific Publishing Company.

Original language	English
Pages (from-to)	479-489
Number of pages	10
Journal	International Journal of Bifurcation and Chaos
Volume	20
Issue number	2
DOIs	https://doi.org/10.1142/S0218127410025557
Publication status	Published - Feb 2010

Keywords

Border-collision bifurcation
Hybrid system
Snap-back-repeller

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10.1142/S0218127410025557

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title = "Bifurcations of snap-back repellers with application to border-collision bifurcations",

abstract = "The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations. {\textcopyright} 2010 World Scientific Publishing Company.",

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author = "Paul Glendinning",

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T1 - Bifurcations of snap-back repellers with application to border-collision bifurcations

AU - Glendinning, Paul

PY - 2010/2

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N2 - The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations. © 2010 World Scientific Publishing Company.

AB - The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations. © 2010 World Scientific Publishing Company.

KW - Border-collision bifurcation

KW - Hybrid system

KW - Snap-back-repeller

U2 - 10.1142/S0218127410025557

DO - 10.1142/S0218127410025557

M3 - Article

VL - 20

SP - 479

EP - 489

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 2

ER -

Bifurcations of snap-back repellers with application to border-collision bifurcations

Abstract

Keywords

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