Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Lajos Lóczi

doi:10.1080/10236198.2014.992786

Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Lajos Lóczi

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

Abstract

© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.

Original language	English (US)
Pages (from-to)	155-196
Number of pages	42
Journal	Journal of Difference Equations and Applications
Volume	21
Issue number	3
DOIs	https://doi.org/10.1080/10236198.2014.992786
State	Published - Jan 7 2015
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05 – 2000000231
Acknowledgements: The project was supported by the European Union and co-financed by the European Social Fund
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1080/10236198.2014.992786

Cite this

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title = "Discretizing the transcritical and pitchfork bifurcations – conjugacy results",

abstract = "{\textcopyright} 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.",

author = "Lajos L{\'o}czi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): FIC/2010/05 – 2000000231 Acknowledgements: The project was supported by the European Union and co-financed by the European Social Fund This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1080/10236198.2014.992786",

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T1 - Discretizing the transcritical and pitchfork bifurcations – conjugacy results

AU - Lóczi, Lajos

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): FIC/2010/05 – 2000000231 Acknowledgements: The project was supported by the European Union and co-financed by the European Social Fund This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2015/1/7

Y1 - 2015/1/7

N2 - © 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.

AB - © 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.

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DO - 10.1080/10236198.2014.992786

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SP - 155

EP - 196

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 3

ER -

Discretizing the transcritical and pitchfork bifurcations – conjugacy results

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