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On the global behavior of some syste...

Lapierre, Evelina Giusti.

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On the global behavior of some systems of difference equations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the global behavior of some systems of difference equations./
Author:	Lapierre, Evelina Giusti.
Description:	189 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
Contained By:	Dissertation Abstracts International74-07B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3557467
ISBN:	9781303005923

On the global behavior of some systems of difference equations.
Lapierre, Evelina Giusti.

On the global behavior of some systems of difference equations. - 189 p.

Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.

Thesis (Ph.D.)--University of Rhode Island, 2013.

This dissertation is an exposition of systems of difference equations. I examine multiple examples of both piecewise and rational difference equations.

ISBN: 9781303005923Subjects--Topical Terms:

515831
Mathematics.

On the global behavior of some systems of difference equations.
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020 $a 9781303005923
035 $a (MiAaPQ)AAI3557467
035 $a AAI3557467
040 $a MiAaPQ $c MiAaPQ
100 1 $a Lapierre, Evelina Giusti. $3 2096723
245 1 0 $a On the global behavior of some systems of difference equations.
300 $a 189 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
500 $a Adviser: Gerasimos Ladas.
502 $a Thesis (Ph.D.)--University of Rhode Island, 2013.
520 $a This dissertation is an exposition of systems of difference equations. I examine multiple examples of both piecewise and rational difference equations.
520 $a In the first two manuscripts, I share the published results of two members of the following family of 81 systems of piecewise linear difference equations: xn+1=xn +ayn+byn+1 =xn+cyn +d,n=0,1,&ldots; where the initial condition (x0, y0) ∈ R2, and where the parameters a, b, c and d are integers between -1 and 1, inclusively. Since each parameter can be one of three values, there are 81 members. Each system is designated a number. The system's number N is given by N=27a+1+9 b+1+3c+1 +d+1+1. .
520 $a The first manuscript is a study of System(2). System(2) results when a = b = c = -1 and d = 0. For System(2), I show that there exists a unique equilibrium solution and exactly two prime period-5 solutions, and that every solution of the system is eventually one of the two prime period-5 solutions or the unique equilibrium solution.
520 $a The second manuscript is a study of System(8). System(8) results when a = b = -1, c = 1 and d = 0. For System(8), I show that there exists a unique equilibrium solution and exactly two prime period-3 solutions, and that except for the equilibrium solution, every solution of the system is eventually one of the two prime period-3 solutions.
520 $a Of the 81 systems, 65 have been studies thoroughly. In Appendix .1, I give the unpublished results of the 21 systems that I studied. In Appendix .2, I list all 81 systems (studied by W. Tikjha, E. Grove, G. Ladas, and E. Lapierre) each with a theorem or conjecture about its global behavior.
520 $a In the third manuscript, I give the published results of the following system of rational difference equations: xn+1=a1 xn+yn yn+1=a2+b2 xn+ynyn ,n=0,1,&ldots; where the parameters and initial conditions are positive real values. I show that the system is permanent and has a unique positive equilibrium which is locally asymptotically stable. I also find sufficient conditions to insure that the unique positive equilibrium is globally asymptotically stable.
520 $a In Appendix .3, I give the unpublished results of the following system of rational difference equations: xn+1=a1 xn+yn yn+1=a2+b2 xn+ynB2xn +yn, n=0,1,&ldots; where the parameters and initial conditions are positive real values. I show that the system is permanent. I also find sufficient conditions to insure that the unique positive equilibrium is globally asymptotically stable.
590 $a School code: 0186.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a University of Rhode Island. $b Mathematics. $3 2096724
773 0 $t Dissertation Abstracts International $g 74-07B(E).
790 $a 0186
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3557467