Date of Award
2009
Degree Type
Dissertation
First Advisor
Orlando Merino
Abstract
For every choice of positive parameters α, β, γ, A, B and C, consider the two difference equations [special characters omitted] and [special characters omitted] In this thesis, it is shown that all solutions to Eqns.(E1) and (E2) converge to the positive equilibrium or to a prime period-two solution. A complete qualitative description of the global behavior of solutions to (El) with nonnegative parameters is also given in this thesis whenever prime period-two solutions exist. Furthermore, a relation is established between local stability of equilibria and slopes of critical curves of planar maps. Then this result is used to give global behavior for nonnegative solutions of the system of difference equations [special characters omitted]with positive parameters. In particular, it is shown that the system has between one and three equilibria, and that the number of equilibria determines global behavior as follows: if there is only one equilibrium, then it is globally asymptotically stable. If there are two equilibria, then one is a local attractor and the other one is nonhyperbolic. If there are three equilibria, then they are linearly ordered in the south-east ordering of the plane, and consist of a local attractor, a saddle point, and another local attractor. In addition, sufficient conditions are given for the system to have a unique equilibrium.
Recommended Citation
Basu, Sukanya, "Global behavior of solutions to a class of second-order rational difference equations" (2009). Open Access Dissertations. Paper 2281.
https://digitalcommons.uri.edu/oa_diss/2281
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