On the Periodic Nature of Solutions to the Reciprocal Difference Equation with Maximum
| dc.contributor.advisor | Dr. John E. Franke, Committee Chair | en_US |
| dc.contributor.advisor | Dr. Stephen Schecter, Committee Member | en_US |
| dc.contributor.advisor | Dr. Xiao B. Lin, Committee Member | en_US |
| dc.contributor.advisor | Dr. James Selgrade, Committee Member | en_US |
| dc.contributor.author | Bidwell, John Charles | en_US |
| dc.date.accessioned | 2010-04-02T19:08:44Z | |
| dc.date.available | 2010-04-02T19:08:44Z | |
| dc.date.issued | 2005-04-05 | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | dissertation | en_US |
| dc.degree.name | PhD | en_US |
| dc.description.abstract | We prove that every positive solution of the difference equation x[subscript n] = max[A[subscript i] ⁄ x[subscript n-i] | i ∈ [1,k]] is eventually periodic, and that the prime period is bounded for all positive initial points. A lower bound, growing faster than polynomially, on the maximum prime period for a system of size k is given, based on a model designed to generate long periods. Conditions for systems to have unbounded preperiods are given. All cases of nonpositive systems, with either the A values and/or initial x values allowed to be negative, are analyzed. For all cases conditions are given for solutions to exist, for the solution to be bounded, and for it to be eventually periodic. Finally, we examine several other difference systems, to see if the methods developed in this paper can be applied to them. | en_US |
| dc.identifier.other | etd-12202004-145236 | en_US |
| dc.identifier.uri | http://www.lib.ncsu.edu/resolver/1840.16/5153 | |
| dc.rights | I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. | en_US |
| dc.subject | reciprocal | en_US |
| dc.subject | difference equation | en_US |
| dc.subject | eventually periodic | en_US |
| dc.subject | preperiod | en_US |
| dc.subject | delay | en_US |
| dc.subject | periodic | en_US |
| dc.subject | maximum | en_US |
| dc.title | On the Periodic Nature of Solutions to the Reciprocal Difference Equation with Maximum | en_US |
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