Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Type
ArticleAuthors
Lóczi, LajosKAUST Grant Number
FIC/2010/05 – 2000000231Date
2015-01-07Online Publication Date
2015-01-07Print Publication Date
2015-03-04Permanent link to this record
http://hdl.handle.net/10754/597995
Metadata
Show full item recordAbstract
© 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 FundPublisher
Informa UK Limitedae974a485f413a2113503eed53cd6c53
10.1080/10236198.2014.992786