On the Global Behavior of the Rational System $\boldsymbol{\displaystyle{ x_{n+1} = \frac{ \alpha_{1} }{ x_{n} + y_{n} } \quad \mathrm{AND} \quad y_{n+1} = \frac{ \alpha_{2} + \beta_{2} x_{n} + y_{n} }{ y_{n} } }}$
DOI:
https://doi.org/10.5644/SJM.08.2.09Keywords:
Bounded solutions, system of rational difference equationsAbstract
We investigate the system of rational difference equations in the title, where the parameters and the initial conditions are positive real numbers. We show that the system is permanent and has a unique positive equilibrium which is locally asymptotically stable. We also find sufficient conditions to insure that the unique positive equilibrium is globally asymptotically stable.
2000 Mathematics Subject Classification. 39A10, 39A11
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