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Dynamics of a max-type system of difference equations

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Abstract

In this paper, we study the following max-type system of difference equations

$$\begin{aligned} x_{n} = \max \left\{ \frac{1}{y_{n-m}} , \frac{\alpha _n}{x_{n-r}}\right\} ,\quad y_{n} = \max \left\{ \frac{1}{x_{n-m}} , \frac{\beta _n}{y_{n-r}}\right\} , \quad n=0,1,\ldots , \end{aligned}$$

where \(\alpha _n,\beta _n\in (0, 1)\) are two sequences with \(\sup \{\max \{\alpha _n,\beta _n\}:n=0,1,\ldots \} <1\), \(r,m\in \{1,2,\ldots \}\) with \(r\ne m\) and the initial values \(x_{-d},y_{-d},x_{-d+1},y_{-d+1}, \ldots , x_{-1}, y_{-1}\in (0,+\infty )\) with \(d=\max \{r,m\}\).

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Authors and Affiliations

  1. College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, China

    Taixiang Sun & Hongjian Xi

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  1. Taixiang Sun
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  2. Hongjian Xi
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Correspondence to Taixiang Sun.

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Project supported by NNSF of China (11461003).

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Sun, T., Xi, H. Dynamics of a max-type system of difference equations. Anal.Math.Phys. 6, 393–402 (2016). https://doi.org/10.1007/s13324-016-0124-x

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  • DOI: https://doi.org/10.1007/s13324-016-0124-x

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