×

Global attractivity of a higher order nonlinear difference equation. (English) Zbl 1081.39005

The authors investigate the global attractivity of a positive equlibrium of equations of the form \(y_{n+1} = (p+qy_n)/(1+y_n+ry_{n-k})\), \(n=0,1,\dots\), where \(p,q,r\) are positive numbers. They show that the unique positive equilibrium globally attracts all positive values of the parameters. The obtained results improve previous ones in this direction.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kocic V.L., Global Behavior of Nonlinear Difference Equations of Higher Order with Application (1993) · Zbl 0787.39001
[2] DOI: 10.1016/S0898-1221(03)00090-7 · Zbl 1077.39004 · doi:10.1016/S0898-1221(03)00090-7
[3] Kulenovic M.R.S., Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures (2002)
[4] DOI: 10.1002/cpa.3160480907 · Zbl 0855.39009 · doi:10.1002/cpa.3160480907
[5] Agarwal R., Theory, Methods and Applications (1992)
[6] DOI: 10.1016/S0362-546X(01)00586-7 · Zbl 1042.39523 · doi:10.1016/S0362-546X(01)00586-7
[7] Kuruklis S.A., Journal of Mathematical Analysis and Applications 18 pp 8719– (1994) · Zbl 0842.39004
[8] Elaydi S.N., An Introduction to Difference Equations (1999) · Zbl 0930.39001
[9] Li W.T., Dynamic Systems and Applications 11 pp 339– (2002)
[10] Su Y.H., Applied Mathematics and Computation
[11] DOI: 10.1080/10236190512331319352 · Zbl 1071.39017 · doi:10.1080/10236190512331319352
[12] Yan X.X., Soochow Journal of Mathematics 29 pp 327– (2003)
[13] DOI: 10.1016/S0096-3003(02)00433-2 · Zbl 1044.39013 · doi:10.1016/S0096-3003(02)00433-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.