Attraktorlokalisierung des Lorenz‐Systems

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik - Tập 67 Số 12 - Trang 649-656 - 1987
Г. А. Леонов1, Aleksandr Bunin2, N. Koksch3
1Leningrader Staatliche Universität, Mathematisch-mechanische Fakultät, CCCP – 190 000
2Kursker Staatliche Pädagogische Hochschule, Lehrstuhl für math. Analysis, CCCP-305 016
3Technische Universität Dresden, Sektion Mathematik, Mommsenstr. 13, DDR-8027 Dresden

Tóm tắt

AbstractIn the present paper that region, in which the (minimal) attractor [2, 3] is situated, is localized in the phase space of the Lorenz system [1, 2] by means of Lyapunov's second method. Being based on these estimations and the results of paper [4] 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 with the numerical results by E. Lorenz [1] shows that for certain parameter regions these estimations practically can not be augmented.

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Tài liệu tham khảo

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ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Tập 67 Số 12

649-656

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