Global stability for mixed monotone systems. (English) Zbl 1162.39009
The author uses the method of embedding a system into a larger monotone system, to obtain again the global stability results of M. Kulenovic and O. Merino [Discrete Contin. Dyn. Syst., Ser. B 6, No. 1, 97–110 (2006; Zbl 1092.37014)]. Then he shows that, for the class of mixed-monotone systems, the global stability can be obtained directly, without embedding.
Reviewer: N. C. Apreutesei (Iaşi)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39A10 | Additive difference equations |
| 39A12 | Discrete version of topics in analysis |
| 37C75 | Stability theory for smooth dynamical systems |
Citations:
Zbl 1092.37014References:
| [1] | Cosner C., Dyn. Contin. Discrete Impuls. Syst. 3 pp 283– (1997) |
| [2] | DOI: 10.1016/j.jde.2005.05.007 · Zbl 1103.34021 · doi:10.1016/j.jde.2005.05.007 |
| [3] | Gouzé J.-L., Rapport de Recherche 894 (1988) |
| [4] | Gouzé J.-L., Nonlinear World 1 pp 23– (1994) |
| [5] | Kulenović M., Dynamics of Second Order Rational Difference Equations (2002) · Zbl 0981.39011 |
| [6] | Kulenović M., Math. Sci. Res. Hot-Line 2 pp 1– (1998) |
| [7] | Kulenović M., Discrete Contin. Dyn. Syst. Series B 6 pp 97– (2006) |
| [8] | DOI: 10.1007/s00285-006-0004-3 · Zbl 1118.65057 · doi:10.1007/s00285-006-0004-3 |
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