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In this paper, we show that the system of difference equations \begin{equation*} x_{n}=\frac{ay_{n-1}^{p}+b\left( x_{n-2}y_{n-1}\right) ^{p-1}}{ cy_{n-1}+dx_{n-2}^{p-1}},\ y_{n}=\frac{\alpha x_{n-1}^{p}+\beta \left( y_{n-2}x_{n-1}\right) ^{p-1}}{\gamma x_{n-1}+\delta y_{n-2}^{p-1}}, \end{equation*} $n \in \mathbb{N}_{0}$ where the parameters $a,b,c,d,\alpha ,\beta ,\gamma ,\delta,p$ and the initial values $x_{-2}$, $x_{-1}$, $y_{-2}$, $y_{-1}$ are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.
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참고문헌 (28)
참고문헌 신청
L. Brand / 1955 / Classroom notes: a sequence defined by a difference equation / Amer. Math. Monthly 62(7):489~492
M. Dehghan / 2011 / Global behaviour of the Riccati difference equation of order two / J. Difference Equ. Appl 17(4):467~477
I. Dekkar / 2017 / Global stability of a third-order nonlinear system of difference equations with period-two coefficients / Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM 111(2):325~347
S. N. Elaydi / 1999 / Undergraduate Texts in Mathematics / Springer-Verlag
M. M. El-Dessoky / 2015 / On the solutions and periodic nature of some systems of rational difference equations / J. Comput. Anal. Appl. 18(2):206~218
M. Dehghan / 2011 / Global behaviour of the Riccati difference equation of order two / J. Difference Equ. Appl 17(4):467~477
I. Dekkar / 2017 / Global stability of a third-order nonlinear system of difference equations with period-two coefficients / Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM 111(2):325~347
S. N. Elaydi / 1999 / Undergraduate Texts in Mathematics / Springer-Verlag
M. M. El-Dessoky / 2015 / On the solutions and periodic nature of some systems of rational difference equations / J. Comput. Anal. Appl. 18(2):206~218
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