Statistical Properties of the Transition to Spatiotemporal Chaos
It is nowaday well established, both theoretically and experimentally, that the chaotic time evolution observed in many natural phenomena may be produced by the non-linear interaction of a small number of degrees of freedom1 In spatially extended systems low dimensional chaos is often associated with relevant spatial effects, such as mode competition, travelling waves, localized oscillations2, but the unpredictable time evolution does not influence the spatial order, that is to say the correlation length is comparable with the size of the system. However an extended system may present a chaotic evolution both in space and time that, instead, implies the presence of many degrees of freedom3. The study of the transition from low dimensional chaos to spatiotemporal chaos is a subject of current interest that is not jet completely understood. For example it is important to investigate whether there are general features that are independent of the specific system under study and whether a thermodynamic description may be appropriate3,4.
KeywordsFourier Mode Cellular Automaton Model Roll Axis Spatial Order Spatiotemporal Chaos
Unable to display preview. Download preview PDF.
- 6a.J. Crutchfield K. Kaneko in “Direction in Chaos”, B. L. Hao (World Scientific Singapore 1987); R. Lima, Bunimovich preprint.Google Scholar
- 8.H. Chate’, B. Nicolaenko, to be published in the proceedings of the conference: “New trends in nonlinear dynamics and pattern forming phenomena”, Cargese 1988;Google Scholar
- 9.B. Nicolaenko, in “The Physics of Chaos and Systems Far From Equilibrium”, M. Duong-Van and B. Nicolaenko, eds. (Nuclear Physics B, proceedings supplement 1988).Google Scholar
- 13.F. Bagnoli, S. Ciliberto, A. Francescato, R. Livi, S. Ruffo, in “Chaos and complexity”, M. Buiatti, S. Ciliberto, R. Livi, S. Ruffo eds., (World Scientific Singapore 1988);Google Scholar
- 13a.F. Bagnoli, S. Ciliberto, A. Francescato, R. Livi, S. Ruffo, in the proceedings of the school on Cellular Automata, Les Houches (1989).Google Scholar
- 14.M. Van Dyke, An Album of Fluid Motion (Parabolic Press, Stanford, 1982);Google Scholar
- 14a.D. J. Tritton, Physical Fluid Dynamics (Van Nostrand Reinold, New York, 1979), Chaps.19–22Google Scholar
- 16a.P. Berg, in “The Physics of Chaos and System Far From Equilibrium”, M. Duong-van and B. Nicolaenko, eds. (Nuclear Physics B, proceedings supplement 1988).Google Scholar
- 17a.A. Pocheau Jour. de Phys. 49, 1127 (1988)I;Google Scholar
- 18.S. Chandrasekar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford 1961;Google Scholar