Intermittency
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In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics (Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency).[1][2]
Experimentally, intermittency appears as long periods of almost periodic behavior interrupted by chaotic behavior. As control variables change, the chaotic behavior become more frequent until the system is fully chaotic. This progression is known as the intermittency route to chaos.
Another kind, on-off intermittency, occurs when a previously transversally stable chaotic attractor with dimension less than the embedding space begins to lose stability. Near unstable orbits within the attractor orbits can escape into the surrounding space, producing a temporary burst before returning to the attractor. [4]
In crisis-induced intermittency a chaotic attractor suffers a
Intermittent behaviour is commonly observed in fluid flows that are
See also
- Pomeau–Manneville scenario
- Crisis (dynamical systems)
- Turbulent flow
- Fluorescence intermittency (blinking) of organic molecules and colloidal quantum dots (nanocrystals)
References
- ^ Mingzhou Ding. Alwyn Scott (ed.). "Intermittency" (PDF). Encyclopedia of Nonlinear Science. Taylor & Francis. Archived from the original (PDF) on 2011-09-27. Retrieved 2006-04-07.
- ^ Edward Ott (2002). Chaos in dynamical systems. Cambridge University Press. p. 323.
- ^ Yves Pomeau and Paul Manneville, Intermittent Transition to Turbulence in Dissipative Dynamical Systems, Commun. Math. Phys. vol. 74, pp. 189–197 1980
- ^ E.Ott and J.C. Sommerer, Blowout bifurcations: the occurrence of riddled basins and on-off intermittency, Physics Letters A, vol. 188, 1994, pp. 39–47
- ^ C. Meneveau and K.R. Sreenivasan, The multifractal nature of turbulent energy dissipation, Journal of Fluid Mechanics, vol. 224, 1991, pp. 429-484
- ^ F. Anselmet, Y. Gagne, E.J. Hopfinger, R.A. Antonia, High-order velocity structure functions in turbulent shear flows, Journal of Fluid Mechanics, vol. 140, 1984, pp. 63-89
- S2CID 245955138.
- Staicu, A. D. (2002). Intermittency in Turbulence (PDF). Eindhoven University of Technology.
- Vassilicos, J. C. (2000). Intermittency in turbulent flows. ISBN 0-521-79221-5.