A note on the differential equations of Gleick-Lorenz

Hirsch, Morris W.

doi:10.1090/S0002-9939-1989-0955996-1

A note on the differential equations of Gleick-Lorenz

Author: Morris W. Hirsch
Journal: Proc. Amer. Math. Soc. 105 (1989), 961-962
MSC: Primary 58F13; Secondary 34C11
DOI: https://doi.org/10.1090/S0002-9939-1989-0955996-1
MathSciNet review: 955996
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for the Gleick-Lorenz equations, every solution in the positive octant blows up.

[Coppel 1965] W. A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, 1965. MR 0190463 (32:7875)
[Deno 1988] C. Deno, University of California at Berkeley, unpublished.
[Gleick 1987] J. Gleick, Chaos, Viking, New York, 1987. MR 1010647 (91d:58152)
[Kamke 1932] E. Kamke, Zur Theorie der systeme gewöhnlicher differential Gleichungen II, Acta. Math. 58 (1932), 57-85. MR 1555344
[Lorenz 1963] E. N. Lorenz, Determinisitc chaotic flow, J. Atmos. Sci. 20 (1963), 130-141.
[Müller 1926] M. Müller, Über das Fundamentaltheorem in der théorie der gewöhnlichen differentialgleichungen, Math. Z. 26 (1926), 619-645.
[Selgrade 1980] J. Selgrade, Asymptotic behavior of solutions to single loop positive feedback systems, J. Differential Equations 38 (1980), 80-103. MR 592869 (82a:34038)