Symbolic vector dynamics approach to initial condition and control parameters estimation of coupled map lattices

In this paper, we extend symbolic dynamics, a standard analytical method for 1-D chaotic map, and initiate a solution to the problem of estimation in coupled map lattices (CMLs) by introducing the symbolic vector dynamics. We develop a novel technique for estimating initial conditions. We also expand the applicable scope of a word-lifting technique for parameter estimation from a 1-D chaotic map to CMLs. Both theoretical and experimental results show that those algorithms can construct one-to-one correspondence between the set of global orbits and the set of admissible codes. Therefore, we provide novel analytical techniques for understanding turbulences in CMLs.