Oscillation and asymptotic stability of two systems of difference equations of rational form. (English) Zbl 1009.39006

Summary: We study the oscillatory behavior and asymptotic stability of the systems of two difference equations of rational form \[ x_{n+1}= {y_n+x_{n-1} y_{n-2}\over y_nx_{n-1}+ y_{n-2}},\;y_{n+1}= {x_n+y_{n-1} x_{n-2} \over x_ny_{n-1}+ x_{n-2}} \] and \[ x_{n+1}= {x_{n-1}+y_ny_{n-2}\over y_nx_{n-1}+ y_{n-2}},\;y_{n+1}= {y_{n-1}+x_nx_{n-2} \over x_ny_{n-1}+ x_{n-2}}. \]


39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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[4] DOI: 10.1080/10236199808808157 · Zbl 0925.39004
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