On the trichotomy character of Xn+1 = (α + βXn + γXn-1)/(A + Xn)

Authors

C. H. Gibbons, University of Rhode Island
M. R.S. Kulenović, University of Rhode Island
G. Ladas, University of Rhode Island
H. D. Voulov, University of Rhode Island

Document Type

Article

Date of Original Version

1-1-2002

Abstract

We show that the equation in the title with nonnegative parameters and nonnegative initial conditions exhibits a trichotomy character concerning periodicity, convergence, and boundedness which depends on whether the parameter γ is equal, less, or greater than the sum of the parameters β and A.

Publication Title, e.g., Journal

Journal of Difference Equations and Applications

Volume

8

Issue

1

Citation/Publisher Attribution

Gibbons, C. H., M. R. Kulenović, G. Ladas, and H. D. Voulov. "On the trichotomy character of Xn+1 = (α + βXn + γXn-1)/(A + Xn)." Journal of Difference Equations and Applications 8, 1 (2002): 75-92. doi: 10.1080/10236190211940.