On the Solutions of Difference Equation Systems with Padovan Numbers

Abstract

In this study, we investigate the form of the solutions of the following rational difference equation systems 

, , such that their solutions are associated with Padovan numbers.


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Y. Yazlik, D. Tollu and N. Taskara, "On the Solutions of Difference Equation Systems with Padovan Numbers," Applied Mathematics, Vol. 4 No. 12A, 2013, pp. 15-20. doi: 10.4236/am.2013.412A002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. P. Agarwal, “Difference Equations and Inequalities,” Marcel Dekker, New York, 2000
[2] M. Aloqeili, “Dynamics of a Rational Difference Equation,” Applied Mathematics and Computation, Vol. 176, No. 2, 2006, pp. 768-774.
http://dx.doi.org/10.1016/j.amc.2005.10.024
[3] T. F. Ibrahim, “On the Third Order Rational Difference equation ,” International Journal of Contemporary Mathematical Sciences, Vol. 4, No. 25-28, 2009, pp. 1321-1334.
[4] R. Khalaf-Allah, “Asymptotic Behaviour and Periodic Naturel of Two Difference Equations,” Ukrainian Mathematical Journal, Vol. 61, No. 6, 2009, pp. 988-993.
http://dx.doi.org/10.1007/s11253-009-0249-2
[5] E. M. Elabbasy, H. A. El-Metwally and E. M. Elsayed, “Global Behavior of the Solutions of Some Difference Equations,” Advances in Difference Equations, Vol. 2011, 2011, p. 28.
http://dx.doi.org/10.1186/1687-1847-2011-28.
[6] E. M. Elsayed, “Solution and Attractivity for a Rational Recursive Sequence,” Discrete Dynamics in Nature and Society, Vol. 2011, 2011, Article ID: 982309.
[7] C. Cinar, “On the Positive Solutions of the Difference Equation System ,” Applied Mathematics and Computation, Vol. 158, No. 2, 2004, pp. 303305. http://dx.doi.org/10.1016/j.amc.2003.08.073
[8] X. Yang, Y. Liu and S. Bai, “On the System of High Order Rational Difference Equations ,” Applied Mathematics and Computation, Vol. 171, No. 2, 2005, pp. 853-856.
http://dx.doi.org/10.1016/j.amc.2005.01.092
[9] A. S. Kurbanli, C. Cinar and I. Yalcinkaya, “On the Behavior of Positive Solutions of the System of Rational Difference Equations,” Mathematical and Computer Modelling, Vol. 53, No.5-6, 2011, pp. 1261-1267.
http://dx.doi.org/10.1016/j.mcm.2010.12.009
[10] E. M. Elsayed, “Solutions of Rational Difference Systems of Order Two,” Mathematical and Computer Modelling, Vol. 55, No. 3-4, 2012, pp. 378-384.
http://dx.doi.org/10.1016/j.mcm.2011.08.012
[11] M. Mansour, M. M. El-Dessoky and E. M. Elsayed, “The Form of the Solutions and Periodicity of Some Systems of Difference Equations,” Discrete Dynamics in Nature and Society, Vol. 2012, 2012, Article ID: 406821.
[12] S. Stevic, “On a System of Difference Equations,” Applied Mathematics and Computation Vol. 218, No. 7, 2011, pp. 3372-3378.
http://dx.doi.org/10.1016/j.amc.2011.08.079
[13] S. Stevic, “On Some Solvable Systems of Difference Equations,” Applied Mathematics and Computation, Vol. 218, No. 9, 2012, pp. 5010-5018.
http://dx.doi.org/10.1016/j.amc.2011.10.068
[14] D. T. Tollu, Y. Yazlik and N. Taskara, “On the Solutions of Two Special Types of Riccati Difference Equation via Fibonacci Numbers,” Advances in Difference Equations, Vol. 2013, 2013, p. 174.
http://dx.doi.org/10.1186/1687-1847-2013-174
[15] A. S. Kurbanli, C. Cinar and D. Simsek, “On the Periodicity of Solutions of the System of Rational Difference Equations ,” Applied Mathematics, Vol. 2, No. 4, 2011, pp. 410-413.
http://dx.doi.org/10.4236/am.2011.24050
[16] A. G. Shannon, P. G. Anderson and A. F. Horadam, “Properties of Cordonnier, Perrin and Van der Laan Numbers,” International Journal of Mathematical Education in Science and Technology, Vol. 37, No. 7, 2006, pp. 825-831. http://dx.doi.org/10.1080/00207390600712554
[17] Benjamin M. M. De Weger, “Padua and Pisa are Exponentially Far Apart,” Publicacions Matematiques, Vol. 41, No. 2, 1997, pp. 631-651.
http://dx.doi.org/10.5565/PUBLMAT_41297_23
[18] M. R. S. Kulenovic and O. Merino, “Discrete Dynamical Systems and Difference Equations with Mathematica,” A CRC Press Company, NewYork, 2002.

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