Global behavior of nonlinear difference equations

Author

Cathy Ann Clark, University of Rhode Island

Date of Award

2004

Degree Type

Dissertation

First Advisor

Mustafa R. S. Kulenovic

Abstract

We investigate the global asymptotic stability, the periodic nature, the rate of convergence, and the bounded character of solutions of two rational difference equations and a system of rational equations. We analyze the behavior of solutions of the equation [special characters omitted]with non-negative parameters and non-negative initial conditions. This is a special case of the more general equation [special characters omitted]and is one of the first third order rational difference equations to be investigated in which all three terms are present in the equation. A thorough analysis of a specific period-two pathology of solutions for the case A = 0 is presented. The behavior of solutions of the system [special characters omitted]with non-negative parameters and non-negative initial conditions is completely characterized for initial conditions in the second and fourth quadrant of the positive equilibrium in the case when neither a nor b is equal to 1. The stability of the Gumovski-Mira equation [special characters omitted]is shown to be preserved when the coefficient b is a periodic sequence with prime period two. The behavior of solutions for the case where the even or odd subsequence of the coefficient is zero is also presented.

Recommended Citation

Clark, Cathy Ann, "Global behavior of nonlinear difference equations" (2004). Open Access Dissertations. Paper 1947.
https://digitalcommons.uri.edu/oa_diss/1947