耦合映象格子的应用符号向量动力学
Applied Symbolic Vector Dynamics of Coupled Map Lattice
摘要：
符号动力学将无限数量的有限长度轨迹划分为有限数量的轨迹集，以简化和粗粒度的方式用有限数量的符号描述系统的动力学。一维混沌映射的符号动力学研究得到了进一步发展，称之为应用符号动力学。本文将研究CML的应用符号向量动力学。基于参考文献中提出的原始贡献。[6]在此基础上，我们将研究CML的遍历性。分析了容许性条件与控制参数的关系，给出了一种基于遍历性的耦合系数估计方法。理论和实验结果表明，我们提供了一个自然的分析技术，了解在CML的连续性。我们的许多发现可以扩展到更广泛的应用。
英文摘要：
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.
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