IJPAM: Volume 53, No. 1 (2009)

ON THE GLOBAL CHARACTER OF THE SYSTEM
$x_{n+1}=\frac{\alpha_{1}+ \gamma_{1}y_{n}}{x_{n}}$ and $y_{n+1}=\frac{\beta_{2} x_{n}+\gamma_{2}y_{n}}{B_2x_{n}+C_2y_{n}}$

E. Camouzis$^1$, G. Ladas$^2$, L. Wu$^3$
$^1$Department of Mathematics
American College of Greece
6, Gravias Street, Aghia Paraskevi, 15342, Athens, GREECE
e-mail: [email protected]
$^{2,3}$Department of Mathematics
University of Rhode Island
Kingston, RI 02881-0816, USA
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.We investigate the global character of solutions of the rational system in the title with nonnegative parameters and with arbitrary positive initial conditions. In particular we obtain necessary and sufficient conditions for all solutions of the system to be bounded. We also show that in a certain region of the parameters every solution of the system converges to a finite limit or to a period-two solution.

Received: March 16, 2009

AMS Subject Classification: 39A10

Key Words and Phrases: boundedness, convergence, period-two convergence, rational systems, stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 1