Solution form of a higher‐order system of difference equations and dynamical behavior of its special case

In this paper we show that the system of difference equations x n = ay n−k + dy n−k x n−(k+l) bx n−(k+l) + cy n−l , y n = αx n−k + δx n−k y n−(k+l) βy n−(k+l) + γx n−l , where n ∈ N 0 , k and l are positive integers, the parameters a, b, c, d, α, β, γ, δ are real numbers and the initial values x −j , y −j , j = 1, k + l, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.

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“…, the general solutions of equations in (2.12) and (2.13) are 17) respectively. Consequently, we get 19) and so 20) and…”

Section: Solvability Of System (15)mentioning

confidence: 99%

Solvability of a system of higher order nonlinear difference equations

Kara

Yazlık

Tollu

2020

Hacettepe Journal of Mathematics and Statistics

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“…1676 YASIN YAZLIK AND M ERVE KARA Quite recently in [14], Haddad et al considered the following system of di¤erence equations…”

Section: Introductionmentioning

confidence: 99%

On a solvable system of difference equations of higher-order with period two coefficients

Yazlık¹,

Kara²

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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We show that the next di¤erence equations system x n+1 = anx n k+1 y n k yn n + n+1 ; y n+1 = bny n k+1 x n k xn n + n+1 ; n 2 N 0 ; where N 0 = N [ f0g, the sequences (an) n2N 0 , (bn) n2N 0 , (n) n2N 0 , (n) n2N 0 are two periodic and the initial conditions x i , y i i 2 f0; 1; : : : ; kg, are nonzero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a 0 = b 1 and a 1 = b 0 .

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“…Haddad et al [7] obtained solution form of a higher-order system of difference equations and dynamical behavior of its special case…”

Section: Introductionmentioning

confidence: 99%