1980 | OriginalPaper | Buchkapitel
Chaos and Turbulence
verfasst von : O. E. Rössler
Erschienen in: Dynamics of Synergetic Systems
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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A special type of turbulence, called boiling type turbulence, can be obtained by coupling a set of identical single-threshold relaxation oscillators in such a manner that the slow variables are locally cross-inhibitory. If the cross-inhibition is overcritical, leading to ‘morphogenesis’ between the slow variables, a sudden slackening occurs wherever the the slowly moving-up ‘skyline’ hits the threshold (with the consequence of a rearrangement of the skyline); and so forth. A simple equation is considered on a ring in a cellular approximation. One cell is not chaotic; two are capable of chaos; three apparently produce higher chaos of the first order; and so forth. In the 3-cellular case, geometrical arguments backed by simulation suggest the presence of a cross-section which is folded over (between one passage and the next) in several independent directions. By implication, the formation of singular sets of Alexandrov type can be expected.