A new characterization of periodic oscillations in periodic difference equations

Ahmad Al-Salman and Ziyad AlSharawi

Chaos, Solitons & Fractals, 2011, vol. 44, issue 11, 921-928

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:11:p:921-928

DOI: 10.1016/j.chaos.2011.07.011

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