Geodesic
Asymptotic behavior of solutions of a rational system of difference equations
Bekker, Miron B.1 ; Bohner, Martin J.2 ; Voulov, Hristo D.3
1 Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
2 Department of Mathematics and Statistics, Missouri S&T, Rolla, MO, USA
3 Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA
Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 379-382.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.007.06.02
Classification : 39A10, 39A20
Keywords: Systems of rational difference equations, global attractors.

Bekker, Miron B. 1 ; Bohner, Martin J. 2 ; Voulov, Hristo D. 3

1 Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
2 Department of Mathematics and Statistics, Missouri S&T, Rolla, MO, USA
3 Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA 
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Bekker, Miron B.; Bohner, Martin J.; Voulov, Hristo D. Asymptotic behavior of solutions of a rational system of difference equations. Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 379-382. doi : 10.22436/jnsa.007.06.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.06.02/

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

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

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

[5] Camouzis, E.; Kent, C. M.; Ladas, G.; Lynd, C. D. 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., Volume 18 (2012), pp. 1205-1252

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