Difference equations with delay

  • Odo Diekmann
  • Stephan A. van Gils
Article
Received:

Abstract

In this note we employ combinatorial arguments to count and classify certain periodic solutions of the delayed difference equationx(n) = f(x(n − k)), withk ≥ 2 given andn ∈ ℤ, The periodic solutions that we consider are formed by combiningk copies of anm- periodic solution of the “ordinary” difference equationx(n) =f(x(n- 1)). We also briefly discuss the possibility of braiding different periodic solutions of the ordinary difference equation into a periodic solution of the delayed version.

Key words

delayed difference equation periodic patterns necklaces 
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Copyright information

© JJIAM Publishing Committee 2000

Authors and Affiliations

  • Odo Diekmann
    • 1
  • Stephan A. van Gils
    • 2
  1. 1.Vakgroep WiskundeUtrecht UniversityUtrechtThe Netherlands
  2. 2.Faculty of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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