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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.

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
37C75 Stability theory for smooth dynamical systems
Full Text: DOI
[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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