Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1997-06-29
Phys. Rev. E 47 (1993) 3122-3127
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Plain TeX, 12 pages, 4 postscript figures included
Scientific paper
10.1103/PhysRevE.47.3122
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems can be described in terms of a one-dimensional map, and previous work has shown how the effect of noise can be modelled by a simple adjustment to the map. Here we undertake an in depth investigation of a particular set of equations, using the methods of stochastic integration. We confirm the prediction of the earlier studies that the noise becomes important when mu|log(epsilon)| = O(1), where mu is the small timescale ratio and \epsilon is the noise level. In addition, we present detailed information about the statistics of the solution when the noise is a dominant effect; the analytical results show excellent agreement with numerical simulations.
Lythe G. D.
Proctor Michael R. E.
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