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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.
On the basis of the symbolic dynamics, the inversed problem of the local coupled map grid system based on the kinematic symplectic sequence is discussed in depth. The properties of the initial estimate of the coupled image system are systematically analyzed in terms of the mathematical properties of the coupling coefficient and the mapping function It is proved that any value of IM on the phase space IM does not converge to the initial value through the inverse iterative process based on the sequence of symbol vectors and its convergence and divergence are directly related to the choice of coupling strength and mapping function. The topological conjugate inverse is not necessarily a contraction mapping, and its overall convergence and divergence is related to the contrast of convergence and divergence in the entire inverse iteration process. The theoretical analysis and the numerical experiment are completely consistent, which shows that the proposed conjugate mapping lattice system The analysis and the algorithm of the problem of value estimation are correct.The feasibility conditions for estimating the initial value of the coupled image system based on symbolic dynamics are discussed in depth and provide an important theoretical basis and experiment for the better analysis and characterization of the physical process of the actual model result.