基于符号动力学的耦合映像格子系统的初值估计

Initial condition estimate of coupled map lattices system based on symbolic dynamics

在符号动力学的基础上,深入探讨了基于动力学符号序列的局部耦合映像格子系统求逆问题.在理论上系统地分析耦合映像系统初值估计的性能与耦合系数及映射函数之间的数学关系,证明相空间IM上的任意取值通过基于符号向量序列的逆迭代过程并不一定收敛至初值,其敛散性与耦合强度和映射函数的选择有直接关系.同时证明了混沌或其拓扑共轭的逆不一定为压缩映射,其总体的敛散性与整个逆迭代过程中的收敛与发散的强度对比有关.理论分析与数值实验结果完全一致,说明本文提出的耦合映像格子系统初值估计问题的分析与算法是正确的.全面深入探讨了基于符号动力学估计耦合映像系统初值的可行性条件,为更好地分析和刻画实际模型的物理过程提供了重要的理论依据与实验结果.

The initial condition estimate of local coupled map lattice system based on given symbolic sequence is researched. The relationships be tween the parameter of coupling strength, the map function and the performance of estimating initial condition are analyzed. It is proved that any value taken from the phase-space I^M does not necessarily converge to the initial vector. There is a direct relationship between convergence property and coupling strength. Moreover, the performances of estimating initial vector are different according to different map functions. The simulation results are completely consistent with theoretical analysis, which shows that the proposed arithmetic for estimating initial vector of coupled map lattice system is correct. The inverse process of coupled map lattice system is fully investigated and the simulation results in this paper provide a theoretical and factual basis for better analysis and description of the physical process of the actual model.