Asymptotic behavior of solutions of a rational system of difference equations
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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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ISRP Style
Miron B. Bekker, Martin J. Bohner, Hristo D. Voulov, Asymptotic behavior of solutions of a rational system of difference equations, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 6, 379--382
AMA Style
Bekker Miron B., Bohner Martin J., Voulov Hristo D., Asymptotic behavior of solutions of a rational system of difference equations. J. Nonlinear Sci. Appl. (2014); 7(6):379--382
Chicago/Turabian Style
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 Applications, 7, no. 6 (2014): 379--382
Keywords
- Systems of rational difference equations
- global attractors.
MSC
References
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[1]
E. Camouzis, G. Ladas, When does local asymptotic stability imply global attractivity in rational equations?, J. Difference Equ. Appl., 12 (2006), 863-885.
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[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)
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[3]
E. Camouzis, M. R. S. Kulenović, G. Ladas, O. Merino, Rational systems in the plane, J. Difference Equ. Appl., 15 (2009), 303-323.
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[4]
E. Camouzis, G. Ladas , Global results on rational systems in the plane, part 1, J. Difference Equ. Appl., 16 (2010), 975-1013.
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[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.