Thermodynamic limit from small lattices of coupled maps

Details Thermodynamic limit from small lattices of coupled maps Thermodynamic limit from small lattices of coupled maps

1999-04-02

arxiv.org/abs/chao-dyn/9904009v1

Phys. Rev. Lett. 83 (1999) 3633--3636

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4 pages, RevTeX, 4 Postscript figures. Submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.83.3633

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. 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.

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