Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Handle URI:
http://hdl.handle.net/10754/597995
Title:
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Authors:
Lóczi, Lajos
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.
Citation:
Lóczi L (2015) Discretizing the transcritical and pitchfork bifurcations – conjugacy results. Journal of Difference Equations and Applications 21: 155–196. Available: http://dx.doi.org/10.1080/10236198.2014.992786.
Publisher:
Informa UK Limited
Journal:
Journal of Difference Equations and Applications
KAUST Grant Number:
FIC/2010/05 – 2000000231
Issue Date:
7-Jan-2015
DOI:
10.1080/10236198.2014.992786
Type:
Article
ISSN:
1023-6198; 1563-5120
Sponsors:
The project was supported by the European Union and co-financed by the European Social Fund
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLóczi, Lajosen
dc.date.accessioned2016-02-25T13:10:35Zen
dc.date.available2016-02-25T13:10:35Zen
dc.date.issued2015-01-07en
dc.identifier.citationLóczi L (2015) Discretizing the transcritical and pitchfork bifurcations – conjugacy results. Journal of Difference Equations and Applications 21: 155–196. Available: http://dx.doi.org/10.1080/10236198.2014.992786.en
dc.identifier.issn1023-6198en
dc.identifier.issn1563-5120en
dc.identifier.doi10.1080/10236198.2014.992786en
dc.identifier.urihttp://hdl.handle.net/10754/597995en
dc.description.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.en
dc.description.sponsorshipThe project was supported by the European Union and co-financed by the European Social Funden
dc.publisherInforma UK Limiteden
dc.subjectconjugacyen
dc.subjectdiscretized bifurcationsen
dc.subjectpitchfork bifurcationen
dc.subjecttopological equivalenceen
dc.subjecttranscritical bifurcationen
dc.titleDiscretizing the transcritical and pitchfork bifurcations – conjugacy resultsen
dc.typeArticleen
dc.identifier.journalJournal of Difference Equations and Applicationsen
dc.contributor.institutionEötvös Loránd University, Budapest, Hungaryen
kaust.grant.numberFIC/2010/05 – 2000000231en
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