Representation of solutions of a second-order system of difference equations in terms of Padovan sequence. (English) Zbl 1447.39001
Summary: This paper deals with the solution, stability character and asymptotic behavior of a rational difference equation where the initial conditions are non zero real numbers, such that their solutions are associated to Padovan numbers. Also, we investigate the two-dimensional case of the equation being considered in this study.
MSC:
| 39A10 | Additive difference equations |
| 39A30 | Stability theory for difference equations |
| 11B37 | Recurrences |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
References:
| [1] | C. W. Clark, A delayed recruitement of a population dynamics with an application to baleen whale population,J Math. Biol.3, 381-391 (1976). · Zbl 0337.92011 |
| [2] | B. M. M. De Weger, Padua and pisa are exponentially far apart,Publ. Mat. Barc. 41, 931-951 (1997). · Zbl 0899.11004 |
| [3] | E. M. Elsayed and T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations,Hacet. J Math. Stat.44, 1361-1390 (2015). · Zbl 1351.39009 |
| [4] | E. M. Elsayed, Solution for systems of difference equations of rational form of order two,Comp. Appl. Math.33, 751-765 (2014). · Zbl 1315.39006 |
| [5] | Y. Halim, Global character of systems of rational difference equations,Electron. J Math. Analysis Appl.3, 204-214 (2015). · Zbl 1390.39012 |
| [6] | Y. Halim, Form and periodicity of solutions of some systems of higher-order difference equations,Math. Sci. Lett.5, 79-84 (2016). |
| [7] | Y. Halim, A system of difference equations with solutions associated to Fibonacci numbers,Int. J Difference Equ.11, 65-77 (2016). |
| [8] | Y. Halim, N. Touafek and Y. Yazlik,Dynamic behavior of a second-order nonlinear rational difference equation,Turk. J Math.39, 1004-1016. (2015). · Zbl 1339.39001 |
| [9] | Y. Halim and M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences,Math. Methods Appl. Sci.39, 2974-2982. (2016). · Zbl 1342.39003 |
| [10] | Y. Halim and J. F. T. Rabago, On some solvable systems of difference equations with solutions associated to Fibonacci numbers,Electron. J Math. Analysis Appl. 5, 166-178. (2017). · Zbl 1375.39029 |
| [11] | V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications.Chapman & Hall, London(1993) · Zbl 0787.39001 |
| [12] | J. F. T. Rabago and Y. Halim, Supplement to the paper of Halim, Tuafek and Elsayed: Part I,Dyn. Contin. Discrete Impulsive Syst. Ser. A24, 121-131. (2017). · Zbl 1361.39004 |
| [13] | J. F. T. Rabago and Y. Halim, Supplement to the paper of Halim, Tuafek and Elsayed: Part II,Dyn. Contin. Discrete Impulsive Syst. Ser. A24, 333-345. (2017). · Zbl 1375.39007 |
| [14] | Y. Halim and J. F. T. Rabago, On the solutions of a second-order difference equations in terms of generalized Padovan sequences,Math. Slovaca68, 625-638. (2018). · Zbl 1417.39006 |
| [15] | S. Stevi´c, Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences,Electron. J Qual. Theory Differ. Equ.67, 1-15. (2014). · Zbl 1324.39004 |
| [16] | N. Touafek, On some fractional systems of difference equations,Iranian J Math. Sci. Info.9, 303-305. (2014). · Zbl 1317.39015 |
| [17] | N. Touafek, On a second order rational difference equation,Hacet. J Math. Stat. 41, 867-874. (2012). · Zbl 1277.39021 |
| [18] | D. T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations,Appl. Math. Comput.233, 310-319(2014). · Zbl 1334.39002 |
| [19] | D. T. Tollu, Y. Yazlik and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers,Adv. Difference Equ.2013, p. 174(2013). · Zbl 1390.39020 |
| [20] | Y. |
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