Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Lóczi, Lajos

Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Type

Article

Authors

Lóczi, Lajos

KAUST Grant Number

FIC/2010/05 – 2000000231

Online Publication Date

2015-01-07

Print Publication Date

2015-03-04

Date

2015-01-07

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.

Acknowledgements

The project was supported by the European Union and co-financed by the European Social Fund