Border collision bifurcation curves and their classification in a family of 1D discontinuous maps

Fabio Tramontana, Laura Gardini

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

In this paper we consider a one-dimensional piecewise linear discontinuous map in canonical form, which may be used in several physical and engineering applications as well as to model some simple financial markets. We classify three different kinds of possible dynamic behaviors associated with the stable cycles. One regime (i) is the same existing in the continuous case and it is characterized by periodicity regions following the period increment by 1 rule. The second one (ii) is the regime characterized by periodicity regions of period increment higher than 1 (we shall see examples with 2 and 3), and by bistability. The third one (iii) is characterized by infinitely many periodicity regions of stable cycles, which follow the period adding structure, and multistability cannot exist. The analytical equations of the border collision bifurcation curves bounding the regions of existence of stable cycles are determined by using a new approach.
Original languageEnglish
Pages (from-to)248-259
Number of pages12
JournalCHAOS, SOLITONS & FRACTALS
Volume44
DOIs
Publication statusPublished - 2011

Keywords

  • Border-Collision bifurcations
  • Discontinuous maps

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