dc.contributor.author | Al-Sharawi, Ziyad | |
dc.contributor.author | Angelos, James | |
dc.contributor.author | Elaydi, Saber | |
dc.date.accessioned | 2020-06-09T07:20:35Z | |
dc.date.available | 2020-06-09T07:20:35Z | |
dc.date.issued | 2008 | |
dc.identifier.citation | Alsharawi, Z., & Angelos, J., & Elaydi, S. (2008). Existence and stability of periodic orbits of periodic difference equations with delays. International Journal of Bifurcation and Chaos, 18(01), 203–217. https://doi.org/10.1142/S0218127408020239 | en_US |
dc.identifier.issn | 1793-6551 | |
dc.identifier.uri | http://hdl.handle.net/11073/16686 | |
dc.description.abstract | In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p, k)-periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky's ordering of the positive integers, and extend Sharkovsky's theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must be divisible by p. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | World Scientific Publishing | en_US |
dc.relation.uri | https://doi.org/10.1142/S0218127408020239 | en_US |
dc.subject | Periodic difference equations | en_US |
dc.subject | Periodic orbits | en_US |
dc.subject | Sharkovsky's theorem | en_US |
dc.subject | Global stability | en_US |
dc.title | Existence and stability of periodic orbits of periodic difference equations with delays | en_US |
dc.type | Peer-Reviewed | en_US |
dc.type | Article | en_US |
dc.type | Preprint | en_US |
dc.identifier.doi | 10.1142/S0218127408020239 | |