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Attraktorlokalisierung des Lorenz-Systems. (Localization of the attractor of the Lorenz system). (German) Zbl 0653.34040

In the present paper that region, in which the (minimal) attractor is situated, is localized in the phase space of the Lorenz system by means of Lyapunov’s second method. Being based on these estimations and the results of paper Differ. Uravn. 22, 1642-1644 (1986; Zbl 0616.34052) a sufficient condition is given that separatrix loops of the saddle \(x=y=z=0\) are missing. Comparison of the bounds for the attractor obtained analytically in this paper shows that for certain parameter regions these estimations practically can not be augmented.

MSC:

34D20 Stability of solutions to ordinary differential equations

Citations:

Zbl 0616.34052
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References:

[1] [Russian Text Ignored.] 1981, 256 c.
[2] The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer Press, New York-Berlin-Heidelberg 1982, 262 p. · Zbl 0504.58001
[3] ; , Attraktoreingrenzung für nichtlineare Systeme, Teubner-Verlag, Leipzig 1987, 197 S. · Zbl 0666.58028
[4] [Russian Text Ignored.] (1986) 9, 1642–1644.
[5] [Russian Text Ignored.] 1979 c. 59–81.
[6] The Lorenz attractor and the problem of turbulence, in Lecture Notes in Mathematics, vol. 565, Springer-Verlag, 1976, pp. 146–158.
[7] [Russian Text Ignored.] 1980, 98 c.
[8] [Russian Text Ignored.] (1983) 5, 861–863.
[9] [Russian Text Ignored.] 1985, T. 2, c. 75–77.
[10] [Russian Text Ignored.] (1985) 5, 860–863.
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