On the Periodicity of Solutions of the System of Rational Difference Equations
Abdullah Selçuk Kurbanli, Cengiz Çinar, Dağistan Şımşek
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DOI: 10.4236/am.2011.24050   PDF    HTML     5,466 Downloads   10,559 Views   Citations

Abstract

In this paper, we have investigated the periodicity of the solutions of the system of difference equations , where .

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A. Kurbanli, C. Çinar and D. Şımşek, "On the Periodicity of Solutions of the System of Rational Difference Equations," Applied Mathematics, Vol. 2 No. 4, 2011, pp. 410-413. doi: 10.4236/am.2011.24050.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] C. ?inar, “On the Positive Solutions of the Difference Equation System ,” Applied Mathematics and Computation, Vol. 158, No. 2, 2004, pp. 303-305. doi:10.1016/j.amc.2003.08.073
[2] G. Papaschinopoulos and C. J. Schinas, “On a System of Two Nonlinear Difference Equations,” Journal of Mathematical Analysis and Applications, Vol. 219, No. 2, 1998, pp. 415-426. doi:10.1006/jmaa.1997.5829
[3] G. Papaschinopoulos and C. J. Schinas, “On the System of Two Difference Equations,” Journal of Mathematical Analysis and Applications, Vol. 273, No. 2, 2002, pp. 294-309. doi:10.1016/S0022-247X(02)00223-8
[4] A. Y. ?zban, “On the System of Rational Difference Equations ,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 833-837. doi:10.1016/j.amc.2006.10.034
[5] A. Y. ?zban, “On the Positive Solutions of the System of Rational Difference Equations ,” Journal of Mathematical Analysis and Applications, Vol. 323, No. 1, 2006, pp. 26-32. doi:10.1016/j.jmaa.2005.10.031
[6] D. Clark and M. R. S. Kulenovi?, “A Coupled System of Rational Difference Equations,” Computers & Mathematics with Applications, Vol. 43, No. 6-7, 2002, pp. 849-867.
[7] D. Clark, M. R. S. Kulenovi? and J. F. Selgrade, “Global Asymptotic Behavior of a Two-Dimensional Diserence Equation Modelling Competition,” Nonlinear Analysis, Vol. 52, No. 7, 2003, pp. 1765-1776. doi:10.1016/S0362-546X(02)00294-8
[8] E. Camouzis and G. Papaschinopoulos, “Global Asym- ptotic Behavior of Positive Solutions on the System of Rational Difference Equations ,” Applied Mathematics Letters, Vol. 17, No. 6, 2004, pp. 733-737. doi:10.1016/S0893-9659(04)90113-9
[9] A. S. Kurbanli, C. ?inar and I. Yalcinkaya, “On the Behavaior of Positive Solutions of the System of Rational Difference Equations ,” Mathematical and Computer Modelling, Vol. 53, No. 5-6, 2011, pp. 1261-1267 doi:10.1016/j.mcm.2010.12.009
[10] A. S. Kurbanli, “On the Behavaior of Solutions of the System of Rational Difference ,” World Applied Sciences Journal, 2010. (In Review).
[11] 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. doi:10.1016/j.amc.2005.01.092
[12] M. R. S. Kulenovi? and Z. Nurkanovi?, “Global Behavior of a Three-Dimensional Linear Fractional System of Difference Equations,” Journal of Mathematical Analysis and Applications, Vol. 310, No. 2, 2005, pp. 673-689.
[13] Y. Zhang, X. Yang, G. M. Megson and D. J. Evans, “On the System of Rational Difference Equations ,” Applied Mathematics and Computation, Vol. 176, No. 2, 2006, pp. 403-408. doi:10.1016/j.amc.2005.09.039
[14] Y. Zhang, X. Yang, D. J. Evans and C. Zhu, “On the Nonlinear Difference Equation System ,” Computers & Mathematics with Applications, Vol. 53, No. 10, 2007, pp. 1561-1566.
[15] I. Yalcinkaya and C. Cinar, “Global Asymptotic Stability of Two Nonlinear Difference Equations ,” Fasciculi Mathematici, Vol. 43, 2010, pp. 171-180.
[16] I. Yalcinkaya, C. ?inar and M. Atalay, “On the Solutions of Systems of Difference Equations,” Advances in Difference Equations, Article ID: 143943, Vol. 2008, 2008. doi: 10.1155/2008/143943
[17] I. Yalcinkaya, “On the Global Asymptotic Stability of a Second-Order System of Difference Equations,” Discrete Dynamics in Nature and Society, Article ID: 860152, Vol. 2008, 2008. doi: 10.1155/2008/860152
[18] B. Iri?anin and S. Stevi?, “Some Systems of Nonlinear Difference Equations of Higher Order with Periodic Solu- tions,” Dynamics of Continuous, Discrete and Impulsive Systems. Series A Mathematical Analysis, Vol. 13, No. 3-4, 2006, pp. 499-507.

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