Manchester Applied Mathematics and Numerical Analysis Seminars

Spring 1999

April 21, 1999, 4.00 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

On the thermodynamic limit for discrete spatio-temporal systems

Dr. Ricardo Carretero-Gonzalez, Centre for Nonlinear Dynamics and its Applications, Univ. College London

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.

Back to the Seminar Homepage

For further info contact either Matthias Heil (, Mark Muldoon ( the seminar secretary (Tel. 0161 275 5800).

Page last modified: December 18, 1998

Back to the department's home page.