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