On the Solutions of Difference Equation Systems with Padovan Numbers

Affiliation(s)

Department of Mathematics, Faculty of Science and Art, Nevsehir University, Nevsehir, Turkey.

Department of Mathematics-Computer Sciences, Science Faculty, Necmettin Erbakan University, Konya, Turkey.

Department of Mathematics, Science Faculty, Selcuk University, Konya, Turkey.

Department of Mathematics, Faculty of Science and Art, Nevsehir University, Nevsehir, Turkey.

Department of Mathematics-Computer Sciences, Science Faculty, Necmettin Erbakan University, Konya, Turkey.

Department of Mathematics, Science Faculty, Selcuk University, Konya, Turkey.

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.

Cite this paper

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

Y. Yazlik, D. Tollu and N. Taskara, "On the Solutions of Difference Equation Systems with Padovan Numbers,"

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.

[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.