Parameter estimate from coupled map lattices based on symbolic vector dynamics

Abstract

Symbolic dynamics, which partitions the infinite number of finite length trajectories into a finite number of trajectory sets, allows a simplified and "coarse-grained" description of the dynamics of a system with a limited number of symbols. In this paper, we further develop the symbolic vector dynamical estimation method in coupled map lattice (CML). We take the CML of Logistic map as an example, to show that the control parameters affect the dynamical characters of symbolic vector sequence. We study the ergodic property of CML by using the inverse function of CML. We give the symbolic vector dynamical description of the initial values, the forbidden words and the control parameters for studying pattern formation in CML. We also give a coupling coefficient estimation approach based on the ergodic property.