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A new characterization of periodic oscillations in periodic difference equations

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  • Al-Salman, Ahmad
  • AlSharawi, Ziyad

Abstract

In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the well-known Sharkovsky’s ordering multiplied by p. On the other hand, we show that the elements of the set Γp of nonmultiples of p are independent in their existence. Moreover, we show the existence of a p-periodic difference equation with infinite Γp-set in which the maps are defined on a compact domain and agree exactly on a countable set. Based on the proposed classification, we give a refinement of Sharkovsky’s theorem for periodic difference equations.

Suggested Citation

  • Al-Salman, Ahmad & AlSharawi, Ziyad, 2011. "A new characterization of periodic oscillations in periodic difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 921-928.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:11:p:921-928
    DOI: 10.1016/j.chaos.2011.07.011
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    Cited by:

    1. AlSharawi, Ziyad, 2022. "Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Al-Ghassani, Asma S. & AlSharawi, Ziyad, 2020. "The effect of maps permutation on the global attractor of a periodic Beverton–Holt model," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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