A solvable system of nonlinear difference equations

Authors : Abdullah ŞAHİNKAYA, İbrahim YALÇINKAYA, Durhasan Turgut TOLLU

Pages : 10-20

View : 21 | Download : 9

Publication Date : 2020-07-30

Article Type : Research Paper

Abstract :In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(x_{n}y_{n}+a);/insert ignore into journalissuearticles values(x_{n}+y_{n}););,y_{n+1}=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(y_{n}z_{n}+a);/insert ignore into journalissuearticles values(y_{n}+z_{n}););,z_{n+1}=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(z_{n}x_{n}+a);/insert ignore into journalissuearticles values(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