Asymptotic behavior of solutions of a rational system of difference equations

Volume 7, Issue 6, pp 379--382 http://dx.doi.org/10.22436/jnsa.007.06.02

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Authors

Miron B. Bekker - Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA. Martin J. Bohner - Department of Mathematics and Statistics, Missouri S&T, Rolla, MO, USA. Hristo D. Voulov - Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA.

Abstract

We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured by Ladas that every positive solution of this system converges to a finite limit. Here we confirm this conjecture.

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Keywords

• Systems of rational difference equations
• global attractors.

MSC

•  39A10
•  39A20

References

• [1] E. Camouzis, G. Ladas, When does local asymptotic stability imply global attractivity in rational equations?, J. Difference Equ. Appl., 12 (2006), 863-885.


• [2] E. Camouzis, G. Ladas, Dynamics of third-order rational difference equations with open problems and conjectures, Advances in Discrete Mathematics and Applications, 5. Chapman & Hall CRC, Boca Raton, FL (2008)


• [3] E. Camouzis, M. R. S. Kulenović, G. Ladas, O. Merino, Rational systems in the plane, J. Difference Equ. Appl., 15 (2009), 303-323.


• [4] E. Camouzis, G. Ladas , Global results on rational systems in the plane, part 1, J. Difference Equ. Appl., 16 (2010), 975-1013.


• [5] E. Camouzis, C. M. Kent, G. Ladas, C. D. Lynd, On the global character of solutions of the system: \(x_{n+1} = \frac{\alpha_1+y_n}{ x_n}\) and \(y_{n+1} = \frac{\alpha_2+\beta_2x_n+\gamma_2y_n}{ A_2+B_2x_n+C_2y_n}\), J. Difference Equ. Appl., 18 (2012), 1205-1252.