Abstract
In this paper we show that the following four-dimensional system of difference equations
where the parameters α, β, γ, δ, ϵ, μ, ξ, ρ ∈ ℤ and the initial values x–i, y–i, z–i, t–i, i ∈ {0, 1}, are real numbers, can be solved in closed forms, extending further some results in literature.
Acknowledgement
This study is a part of the first author’s Ph.D. Thesis.
Communicated by Michal Fečkan
References
[1] Bao, H.: Dynamical behavior of a system of second-order nonlinear difference equations, Int. J. Differ. Equations (2015), Art. ID 679017.10.1155/2015/679017Search in Google Scholar
[2] Boulouh, M.—Touafek, N.—Tollu, D. T.: On the behavior of the solutions of an abstract system of difference equations, J. Appl. Math. Comput. 68 (2022), 2937–2969.10.1007/s12190-021-01641-7Search in Google Scholar
[3] Dekkar, I.—Touafek, N.—Din, Q.: On the global dynamics of a rational difference equation with periodic coefficients, J. Appl. Math. Comput. 60 (2019), 567–588.10.1007/s12190-018-01227-wSearch in Google Scholar
[4] Elsayed, E. M.: On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath. 7(6) (2014), 1–26.Search in Google Scholar
[5] Gümüş, M.—Abo-Zeid, R.: An explicit formula and forbidden set for a higher order difference equation, J. Appl. Math. Comput. 63 (2020), 133–142.10.1007/s12190-019-01311-9Search in Google Scholar
[6] Halim, Y.—Berkal, M.—Khelifa, A.: On a three-dimensional solvable system of difference equations, Turkish J. Math. 44(4) (2020), 1263–1288.10.3906/mat-2001-40Search in Google Scholar
[7] Hamioud, H.—Dekkar, I.—Touafek, N.: Solvability of a third-order system of nonlinear difference equations via generalized Fibonacci sequence, Miskolc Math. Notes 25 (2024), 271–285.10.18514/MMN.2024.4340Search in Google Scholar
[8] Kara, M.—Yazlik, Y.: Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients, Math. Slovaca 71(5) (2021), 1133–1148.10.1515/ms-2021-0044Search in Google Scholar
[9] Kara, M.—Yazlik, Y.: Solvable three-dimensional system of higher-order nonlinear difference equations, Filomat 36(10) (2022), 3449–3469.10.2298/FIL2210449KSearch in Google Scholar
[10] Kara, M.—Yazlik, Y.: On a solvable system of rational difference equations of higher order, Turkish J. Math. 46(2) (2022), 587–611.Search in Google Scholar
[11] Kara, M.—Yazlik, Y.: On the solutions of three-dimensional system of difference equations via recursive relations of order-two and applications, J. Appl. Math. Comput. 12(2) (2022), 736–753.10.11948/20210305Search in Google Scholar
[12] Khelifa, A.—Halim, Y.: Global behavior of p-dimensional difference equations system, Electron. Res. Arch. 29(5) (2021), 3121–3139.10.3934/era.2021029Search in Google Scholar
[13] Stevic, S.—Alghamdi, M. A.—Alotaibi, A.—Elsayed, E. M.: Solvable product type of difference equations of second order, Electron. J. Differential Equations 169 (2015), 1–20.Search in Google Scholar
[14] Stevic, S.: Product-type system of difference equations of second-order solvable in closed form, Electron. J. Qual. Theory Differ. Equ. 56 (2015), 1–16.10.14232/ejqtde.2015.1.56Search in Google Scholar
[15] Tollu, D. T.—Yazlik, Y.—Taskara, N.: On a solvable nonlinear difference equation of higher order, Turkish J. Math. 42(4) (2018), 1765–1778.10.3906/mat-1705-33Search in Google Scholar
[16] Tollu, D. T.—Yalcinkaya, I.: Global behavior of a three-dimensional system of difference equations of order-three, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(1) (2019), 1–16.10.31801/cfsuasmas.443530Search in Google Scholar
[17] Touafek, N.—Elsayed, E. M.: On the periodicity of some systems of nonlinear difference equations, Bull. Math. Soc. Sci. Math. Roum. 55(103) (2012), 217–224.Search in Google Scholar
[18] Yazlik, Y.—Tollu, D. T.—Taskara, N. On the solutions of a three-dimensional system of difference equations, Kuwait J. Sci. 43(1) (2016), 95–111.Search in Google Scholar
© 2024 Mathematical Institute Slovak Academy of Sciences
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- Intervals of posets of a zero-divisor graph
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- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
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- Relative versions of star-Menger property
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