Dynamics of a piecewise linear map with a gap

SJ Hogan, L Higham, TCL Griffin

Research output: Contribution to journalArticle (Academic Journal)peer-review

53 Citations (Scopus)


In this paper, we consider periodic solutions of discontinuous non-smooth maps. We show how the fixed points of a general piecewise linear map with a discontinuity ('a map with a gap') behave under parameter variation. We show in detail all the possible behaviours of period 1 and period 2 solutions. For positive gaps, we find that period 2 solutions can exist independently of period 1 solutions. Conversely, for negative gaps, period 1 and period 2 solutions can coexist. Higher periodic orbits can also exist and be stable and we give several examples of how these solutions behave under parameter variation. Finally, we compare our results with those of Jain & Banerjee (Jain & Banerjee 2003 Int. J. Bifurcat. Chaos 13, 3341 3351) and Banerjee et al. (Banerjee et al. 2004 IEEE Trans. Circ. Syst. II 51, 649 654) and explain their numerical simulations.
Translated title of the contributionDynamics of a piecewise linear map with a gap
Original languageEnglish
Pages (from-to)49 - 65
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume463 (2077)
Publication statusPublished - Jan 2007

Bibliographical note

Publisher: Royal Society


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