Coherence and Large-Scale Pattern Formation in Coupled Logistic-Map Lattices via Computer Algebra Systems

Three quantitative measures of the spatiotemporal behavior of the coupled map lattices: reduced density matrix, reduced wave function, and an analog of particle number, have been introduced. Making extensive use of two computer algebra systems (Maxima and Mathematica) various properties of the above mentioned parameters have been thoroughly studied. Their behavior suggests that the logistic coupled-map lattices approach the states which resemble the condensed states of systems of Bose particles. In addition, pattern formation in two-dimensional coupled map lattices based on the logistic mapping has been investigated with respect to the non-linear parameter, the diffusion constant and initial as well as boundary conditions.