The global stability, boundedness, and periodicity character of certain difference equations

Author

Michael Alexander Radin, University of Rhode Island

Date of Award

2001

Degree Type

Dissertation

First Advisor

Edward A. Grove

Abstract

We study the global stability, the boundedness nature, and the periodic character of the positive solutions of the difference equation [special characters omitted]where the parameters α and β are positive real numbers and the initial conditions x−1 and x0 are arbitrary non-negative real numbers. This problem was proposed by Dr. Richard Levins of the Harvard School of Public Health as a population model in Mathematical Biology. We consider α to be the immigration rate and β to be the population growth rate. We will also investigate the periodic character and the boundedness nature of all positive solutions of following two max - type difference equations: [special characters omitted]and [special characters omitted]where [special characters omitted] is a sequence of positive real numbers with prime period three and the initial conditions x−1 and x0 are arbitrary positive real numbers.

Recommended Citation

Radin, Michael Alexander, "The global stability, boundedness, and periodicity character of certain difference equations" (2001). Open Access Dissertations. Paper 1777.
https://digitalcommons.uri.edu/oa_diss/1777