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

Abstract

The initial condition estimate of local coupled map lattice system based on given symbolic sequence is researched. The relationships between 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. © 2009 Chin.Phys.Soc.

在符號動力學的基礎上,深入探討了基于動力學符號序列的局部耦合映像格子系統求逆問題.在理論上系統地分析耦合映像系統初值估計的性能與耦合系數及映射函數之間的數學關系,證明相空間IM上的任意取值通過基于符號向量序列的逆迭代過程并不一定收斂至初值,其斂散性與耦合強度和映射函數的選擇有直接關系.同時證明了混沌或其拓撲共軛的逆不一定為壓縮映射,其總體的斂散性與整個逆迭代過程中的收斂與發散的強度對比有關.理論分析與數值實驗結果完全一致,說明本文提出的耦合映像格子系統初值估計問題的分析與算法是正確的.全面深入探討了基于符號動力學估計耦合映像系統初值的可行性條件,為更好地分析和刻畫實際模型的物理過程提供了重要的理論依據與實驗結果.