A solvable system of nonlinear difference equations

Year 2020, Volume: 2 Issue: 1, 10 - 20, 30.07.2020

Abdullah Şahinkaya İbrahim Yalçınkaya , Durhasan Turgut Tollu

Abstract

In this paper, we show that the following systems of nonlinear difference equations

x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀

where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form. Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.

Keywords

Asymptotic behavior, explicit solution, nonlinear difference equation, system

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