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 JAMP  Vol.3 No.7 , July 2015
On a System of Second-Order Nonlinear Difference Equations
Abstract: This paper is concerned with dynamics of the solution to the system of two second-order nonlinear difference equations , , , where , , , i = 0, 1. Moreover, the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some numerical examples are considered to show the results obtained.
Cite this paper: Bao, H. (2015) On a System of Second-Order Nonlinear Difference Equations. Journal of Applied Mathematics and Physics, 3, 903-910. doi: 10.4236/jamp.2015.37110.
References

[1]   Papaschinopoulos, G. and Schinas, C.J. (1998) On a System of Two Nonlinear Difference Equations. Journal of Mathematical Analysis and Applications, 219, 415-426.
http://dx.doi.org/10.1006/jmaa.1997.5829

[2]   Clark, D., Kulenovic, M.R.S. and Selgrade, J.F. (2003) Global Asymptotic Behavior of a Two-Dimensional Difference Equation Modelling Competition. Nonlinear Analysis, 52, 1765-1776.
http://dx.doi.org/10.1016/S0362-546X(02)00294-8

[3]   Clark, D. and Kulenovic, M.R.S. (2003) A Coupled System of Rational Difference Equations. Computers and Mathematics with Applications, 43, 849-867. http://dx.doi.org/10.1016/S0898-1221(01)00326-1

[4]   Yang, X. (2005) On the System of Rational Difference Equations . Journal of Mathematical Analysis and Applications, 307, 305-311. http://dx.doi.org/10.1016/j.jmaa.2004.10.045

[5]   Zhang, Q., Yang, L. and Liu, J. (2012) Dynamics of a System of Rational Third-Order Difference Equation. Advances in Difference Equations, 136, 1-8. http://dx.doi.org/10.1186/1687-1847-2012-136

[6]   Zhang, Q., Liu, J. and Luo, Z. (2015) Dynamical Behavior of a System of Third-Order Rational Difference Equation. Discrete Dynamics in Nature and Society, 2015, Article ID: 530453.
http://dx.doi.org/10.1155/2015/530453

[7]   Ibrahim, T.F. (2012) Two-Dimensional Fractional System of Nonlinear Difference Equations in the Modeling Competitive Populations. International Journal of Basic & Applied Sciences, 12, 103-121.

[8]   Din, Q., Qureshi, M.N. and Khan, A.Q. (2012) Dynamics of a Fourth-Order System of Rational Difference Equations. Advances in Difference Equations, 2012, 215.
http://dx.doi.org/10.1186/1687-1847-2012-215

[9]   Kocic, V.L. and Ladas, G. (1993) Global Behavior of Nonlinear Difference Equations of Higher Order with Application. Kluwer Academic Publishers, Dordrecht. http://dx.doi.org/10.1007/978-94-017-1703-8

[10]   Liu, K., Zhao, Z., Li, X. and Li, P. (2011) More on Three-Dimensional Systems of Rational Difference Equations. Discrete Dynamics in Nature and Society, 2011, Article ID: 178483.

[11]   Ibrahim, T.F. and Zhang, Q. (2013) Stability of an Anti-Competitive System of Rational Difference Equations. Archives Des Sciences, 66, 44-58.

[12]   Zayed E.M.E. and El-Moneam, M.A. (2011) On the Global Attractivity of Two Nonlinear Difference Equations. Journal of Mathematical Sciences, 177, 487-499.
http://dx.doi.org/10.1007/s10958-011-0474-8

[13]   Touafek, N. and Elsayed, E.M. (2012) On the Periodicity of Some Systems of Nonlinear Difference Equations. Bulletin Mathématiques de la Société des Sciences Mathématiques de Roumanie, 2, 217-224.

[14]   Touafek, N. and Elsayed, E.M. (2012) On the Solutions of Systems of Rational Difference Equations. Mathematical and Computer Modelling, 55, 1987-1997. http://dx.doi.org/10.1016/j.mcm.2011.11.058

[15]   Kalabusic, S., Kulenovic, M.R.S. and Pilav, E. (2011) Dynamics of a Two-Dimensional System of Rational Difference Equations of Leslie-Gower Type. Advances in Difference Equations, 2011, 29.
http://dx.doi.org/10.1186/1687-1847-2011-29

[16]   Ibrahim, T.F. (2012) Boundedness and Stability of a Rational Difference Equation with Delay. Revue Roumaine de Mathématiques Pures et Appliquées, 57, 215-224.

[17]   Ibrahim, T.F. and Touafek, N. (2013) On a Third-Order Rational Difference Equation with Variable Coefficients. DCDIS Series B: Applications & Algorithms, 20, 251-264.

[18]   Ibrahim, T.F. (2013) Oscillation, Non-Oscillation, and Asymptotic Behavior for Third Order Nonlinear Difference Equations. Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 20, 523-532.

[19]   Zhang, Q. and Zhang, W. (2014) On a System of Two High-Order Nonlinear Difference Equations? Advances in Mathematical Physics, 2014, Article ID: 729273.

[20]   Pituk, M. (2002) More on Poincare’s and Peron’s Theorems for Difference Equations. Journal Difference Equations and Applications, 8, 201-216. http://dx.doi.org/10.1080/10236190211954

 
 
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