Discontinuous Bifurcations of Periodic Solutions

R.I. Leine; D.H. Campen, van

doi:10.1016/S0895-7177(02)00124-3

Discontinuous Bifurcations of Periodic Solutions

R.I. Leine, D.H. Campen, van

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

71 Citations (Scopus)

Abstract

This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix leadto jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuousbifurcation. Numerical examples show discontinuous fold and symmetry-breaking bifurcations. The discontinuous fold bifurcation can connect stable branches tobranches with infinitely unstable periodic solutions.

Original language	English
Pages (from-to)	259-273
Journal	Mathematical and Computer Modelling
Volume	36
Issue number	3
DOIs	https://doi.org/10.1016/S0895-7177(02)00124-3
Publication status	Published - 2002

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title = "Discontinuous Bifurcations of Periodic Solutions",

abstract = "This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix leadto jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuousbifurcation. Numerical examples show discontinuous fold and symmetry-breaking bifurcations. The discontinuous fold bifurcation can connect stable branches tobranches with infinitely unstable periodic solutions.",

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AB - This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix leadto jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuousbifurcation. Numerical examples show discontinuous fold and symmetry-breaking bifurcations. The discontinuous fold bifurcation can connect stable branches tobranches with infinitely unstable periodic solutions.

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DO - 10.1016/S0895-7177(02)00124-3

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VL - 36

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EP - 273

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

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Discontinuous Bifurcations of Periodic Solutions

Abstract

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