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    Discretizing the transcritical and pitchfork bifurcations – conjugacy results

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    Type
    Article
    Authors
    Lóczi, Lajos
    KAUST Grant Number
    FIC/2010/05 – 2000000231
    Date
    2015-01-07
    Online Publication Date
    2015-01-07
    Print Publication Date
    2015-03-04
    Permanent link to this record
    http://hdl.handle.net/10754/597995
    
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    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.
    Sponsors
    The project was supported by the European Union and co-financed by the European Social Fund
    Publisher
    Informa UK Limited
    Journal
    Journal of Difference Equations and Applications
    DOI
    10.1080/10236198.2014.992786
    ae974a485f413a2113503eed53cd6c53
    10.1080/10236198.2014.992786
    Scopus Count
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