Manchester Applied Mathematics and Numerical Analysis SeminarsSpring 1999 |
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Lecture Theatre OF/B9 Oddfellows Hall (Material Science)
We characterise the chaotic behaviour in large spatio-temporal systems by estimating the Lyapunov spectrum from its rescaled counterpart obtained from sub-system information. We discuss a new, more accurate, rescaling technique and its properties. We consider the evolution in tangent space either given explicitly or reconstructed from time-series. We investigate the effects on replacing a large, and potentially infinite, system by a small truncated version with random boundary conditions. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.
For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).