Discretizing the transcritical and pitchfork bifurcations – conjugacy results

Lajos Lóczi

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)155-196
Number of pages42
JournalJournal of Difference Equations and Applications
Volume21
Issue number3
DOIs
StatePublished - Jan 7 2015
Externally publishedYes

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