Applied Symbolic Vector Dynamics of Coupled Map Lattice

TL;DR

This paper investigates the applied symbolic vector dynamics of coupled map lattices (CML), analyzing their ergodic properties and providing a coupling coefficient estimation method to understand turbulence phenomena.

Contribution

It introduces a novel analytical technique for studying turbulence in CML based on symbolic vector dynamics and ergodic properties, extending previous work.

Findings

Established the ergodic property of CML.

Developed a coupling coefficient estimation method.

Validated results through theoretical and experimental analysis.

Abstract

Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The study of symbolic dynamics in 1D chaotic map has been further developed and is named as the applied symbolic dynamics. In this paper, we will study the applied symbolic vector dynamics of CML. Based on the original contribution proposed in Refs.[6], we will study the ergodic property of CML. We will analyze the relation between admissibility condition and control parameters, and then give a coupling coefficient estimation method based on the ergodic property. Both theoretical and experimental results show that we provide a natural analytical technique for understanding turbulences in CML. Many of our findings could be expanded to a wider range of application.