Solutions of Some Difference Equations Systems and Periodicity

  • Elsayed M. Elsayed King Abdulaziz University
  • Faris Alzahrani King Abdulaziz University
  • Ibrahim Abbas King Abdulaziz University
  • N. H. Alotaibi King Abdulaziz University
Keywords: Difference Equation, Periodic Solutions, System of Difference Equations

Abstract

In this article, analysis and investigation have been conducted on the periodic nature as well as the type of the solutions of the subsequent schemes of rational difference equations

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with a nonzero real numbers initial conditions.

Author Biographies

Elsayed M. Elsayed, King Abdulaziz University

Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Faris Alzahrani, King Abdulaziz University

Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Ibrahim Abbas, King Abdulaziz University

Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

N. H. Alotaibi, King Abdulaziz University

1Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

References

A. M. Ahmed,On the dynamics of a systemof rational difference equation, Dynamics of Continuous, Discrete and Impulsive Systems Series A Mathematical Analysis, 21 (2014), 487-506.

M. Alghamdi, E. M. Elsayed and M. M. El-Dessoky, On the Solutions of Some Systems of Second Order Rational Difference Equations, Life Sci J., 10 (3) (2013), 344-351.

S. Araci, Existence and multiplicity of positive solutions for boundary-value problems of non-linear fractional differential equations, Proc. Jangjeon Math. Soc., 17 (2) (2014), 247-258.

A. Asiri, E. M. Elsayed, and M. M. El-Dessoky, On the Solutions and Periodic Nature of Some Systems of Difference Equations, Journal of Computational and Theoretical Nanoscience, 12 (2015), 1—8.

H. Bao, On a System of Second-Order Nonlinear difference Equations, Journal of Applied Mathematics and Physics, 3 (2015), 903-910

C. Cinar, I. Yalçinkaya and R. Karatas, On the positive solutions of the difference equation system xn+1 = m/yn, yn+1 = pyn/xn?1yn?1, J. Inst. Math. Comp. Sci., 18 (2005), 135-136.

Q. Din, On a system of rational difference equation, Demonstratio Mathematica Vol. XLVII (2) (2014), 324-335.

Q. Din, and E. M. Elsayed, Stability analysis of a discrete ecological model, Computational Ecology and Software 4 (2) (2014), 89—103.

E. M. Elabbasy and E. M. Elsayed, Global attractivity and periodic nature of a difference equation, World Appl. Sci. J., 12 (1) (2011), 39—47.

M. M. El-Dessoky, and E. M. Elsayed, On the solutions and periodic nature of some systems of rational difference equations, J. Comput. Anal. Appl., 18 (2) (2015), 206-218.

E. M. Elsayed, On the solutions of a rational system of difference equations, Fasciculi Mathematici, 45 (2010), 25—36.

E. M. Elsayed, Solutions of rational difference system of order two, Math. Comput. Mod., 55 (2012), 378—384.

E.M. Elsayed, Behavior and expression of the solutions of some rational difference equations, J. Comput. Anal. Appl., 15 (1) (2013), 73-81.

E. M. Elsayed, Solution for systems of difference equations of rational form of order two, Comput. Appl. Math., 33 (3) (2014), 751-765.

E. M. Elsayed, On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (6) (2014), 1450067, (26 pages).

E. M. Elsayed, New method to obtain periodic solutions of period two and three of a rational difference equation, Nonlinear Dynamics 79 (1) (2015), 241-250.

E. M. Elsayed and H. El-Metwally, Stability and solutions for rational recursive sequence of order three, J. Comput. Anal. Appl., 17 (2) (2014), 305—315.

E. M. Elsayed and H. El-Metwally, Global behavior and periodicity of some difference equations, J. Comput. Anal. Appl., 19 (2) (2015), 298-309.

H. El-Metwally and E. M. Elsayed, Form of solutions and periodicity for systems of difference equations, J. Comput. Anal. Appl., 15(5) (2013), 852-857.

E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall / CRC Press, 2005.

T. F. Ibrahim and N. Touafek, On a third order rational difference equation with variable coefficients, Dyn. Cont. Disc. Impu. Syst., Appl. Algo., 20 (2013) 251-264.

A. S. Kurbanli, C. Cinar and I. Yalç?nkaya, On the behavior of positive solutions of the system of rational difference equations, Math. Comp. Mod., 53 (2011), 1261- 1267.

A. Kurbanli, C. Cinar andM. Erdo?gan, On the behavior of solutions of the system of rational difference equations xn+1 = xn?1 xn?1yn?1, yn+1 = yn?1 yn?1xn?1, zn+1 = xn zn?1yn , Applied Mathematics 2 (2011), 1031-1038.

K. Liu, P. Li and W. Zhong, On a system of rational difference equationsxn+1 = xn?1/ynxn?1 ?1, yn+1 = yn?1/xnyn?1 ?1, zn+1 = 1/ynzn?1 Fasciculi Mathematici, 51(2013),105-114.

A. Y. Ozban, On the system of rational difference equations xn+1 = a/yn?3, yn+1 = byn?3/xn?q yn?q, Appl. Math. Comp., 188(1) (2007), 833-837.

M. N. Qureshi, A. Q. Khan and Q. Din, Global behavior of third order system of rational difference equations, Int. J. Eng. Res. Tech., 2 (5) (2013), 2182-2191.

M. Mansour, M. M. El-Dessoky and E. M. Elsayed, On the solution of rational systems of difference equations, J. Comput. Anal. Appl., 15 (5) (2013), 967-976.

N. Touafek and E. M. Elsayed, On a second order rational systems of difference equation, Hokkaido Mathematical Journal, 44 (1) (2015), 29—45..

I. Yalç?nkaya, On the global asymptotic stability of a second-order system of difference equations, Disc. Dyn. Nat. Soc., Vol. 2008, Article ID 860152, 12 pages.

I. Yalç?nkaya, On the global asymptotic behavior of a system of two nonlinear difference equations, ARS Combinatoria, 95 (2010), 151-159.

I. Yalç?nkaya, C. Cinar and M. Atalay, On the solutions of systems of difference equations, Advances in Difference Equations, Vol. 2008, Article ID 143943, 9 pages, doi: 10.1155/2008/ 143943.

X. Yang, On the system of rational difference equations xn = A+yn?1/xn?pyn?q, yn = A + xn?1/xn?ryn?s, J. Math. Anal. Appl., 307 (2005), 305—311.

X. Yang, Y. Liu and S. Bai, On the system of high order rational difference equations xn = a/yn?p, yn = byn?p/xn?q yn?q, Appl. Math. Comp., 171(2) (2005), 853-856.

E. M. E. Zayed andM. A. El-Moneam, On the rational recursive sequence xn+1 = axn ? bxn cxn?dxn?k , Comm. Appl. Nonlinear Analysis, 15 (2008), 47-57.

D. Zhang, W. Ji, L. Wang, and X. Li, On the Symmetrical System of Rational Difference Equation xn+1 = A+yn?k/yn, yn+1 = A+xn?k/xn, AppliedMathematics,4 (2013), 834-837.

O.Zkan and A.S.Kurbanli, On a system of difference equation, Dis. Dyn. Net. Soc., Volume 2013 (2013) , Article ID 970316, 7 pages.

Published
2019-01-31
How to Cite
Elsayed, E., Alzahrani, F., Abbas, I., & Alotaibi, N. H. (2019). Solutions of Some Difference Equations Systems and Periodicity. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8247-8261. https://doi.org/10.24297/jam.v16i0.8057
Section
Articles