On the Global Character of the Rational System $\boldsymbol{\displaystyle{ x_{n+1}=\frac{\alpha_1 }{A_1+ B_1 x_n + y_{n}} \quad \mathrm{AND} \quad y_{n+1}=\frac{\alpha_2+\beta_2 x_n}{A_2+B_2 x_n+C_2 y_n}}}$
DOI:
https://doi.org/10.5644/SJM.08.2.10Keywords:
Boundedness, boundedness characterization, global stability, periodicity, patterns of boundedness, rational difference equations, rational systemsAbstract
In this paper we investigate the global stability character of the rational system in the title with the parameters $B_1, B_2, A_2+C_2$ positive, the parameters $A_1,\alpha_2,\beta_2, A_2, C_2$ nonnegative, and with arbitrary nonnegative initial conditions such that the denominators are always positive.
2000 Mathematics Subject Classification. 39A10
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