CRITICAL-BEHAVIOR AND MEAN-FIELD THEORY OF COUPLED MAP LATTICES

We use methods of statistical physics to study the properties of a one-dimensional lattice of coupled tent maps. Statistical properties are calculated from an ensemble of random initial values. The dynamical phase transition occuring in the model can be described in terms of a directed percolation process. Phase diagrams are calculated using two different approximations of mean-field type and compared to direct numerical interactions of finite lattices. The critical behaviour is characterized by finite size scaling expressions that allow us to extract critical exponents from small lattices. Some indications of universality is observed. © 1990 IOP Publishing Ltd.