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Global stability of a third-order nonlinear system of difference equations with period-two coefficients

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The main objective of this paper is to study the global behavior of the following third-order rational system of difference equations

$$\begin{aligned} x_{n+1}=\frac{p_n+y_n}{p_n+y_{n-2}}, \ \ y_{n+1}=\frac{q_n+x_n}{q_n+x_{n-2}}, \qquad n=0,1,2,\ldots , \end{aligned}$$

where \(\{p_n\}\) and \(\{q_n\}\) are 2-periodic sequences of positive numbers, and the initial values \(x_{-i},\, y_{-i} \in [0, \infty )\), for \(i=0,1,2\).

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Authors and Affiliations

  1. LMAM Laboratory, Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria

    Imane Dekkar & Nouressadat Touafek

  2. Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, Nevsehir, Turkey

    Yasin Yazlik

Authors
  1. Imane Dekkar
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  2. Nouressadat Touafek
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  3. Yasin Yazlik
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Correspondence to Nouressadat Touafek.

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Dekkar, I., Touafek, N. & Yazlik, Y. Global stability of a third-order nonlinear system of difference equations with period-two coefficients. RACSAM 111, 325–347 (2017). https://doi.org/10.1007/s13398-016-0297-z

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