Periodicity and solutions for some systems of nonlinear rational difference equations

Year 2015, Volume: 44 Issue: 6, 1361 - 1390, 01.12.2015

E.m. Elsayed T.f. Ibrahim

Abstract

In this paper, we investigated the periodic nature and the form of the
solutions of nonlinear di􏳸erence equations systems of order three

$$x_{n+1}=\dfrac{x_{n-2}y_{n-1}}{y_n(\pm 1\pm x_{n-2}y_{n-1})}, y_{n+1}=\dfrac{y_{n-2}x_{n-1}}{x_n(\pm 1\pm y_{n-2}x_{n-1})},$$

with initial conditions $x_{-2}, x_{-1}, x_0,y_{-2}, y_{-1}$ and $y_0$ are nonzero real numbers. 

Keywords

recursive sequences, stability, periodic solution, difference equation, periodic solution of difference equation, system of difference equation

References

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