从耦合映象格子中粗略恢复初值的统计特性

A statistical property to recover coarsely initial conditions from coupled map lattices

耦合映象格子用于信号处理研究时 ,从中恢复出初始条件是一个非常重要的问题 .提出一种粗略恢复格点初值的方法 ,数值实验表明 ,动力学函数使用Logistic映射时 ,在映象过程不存在噪声的情况下 ,恢复的整个格子初始信号平均值等于给定信号分布的真实平均值 ,而恢复信号的方差小于给定信号的真实方差 .将耦合看作是对独立映射的一种变换 ,对此作了初步解释 ,同时发现Logistic映射不同参数下的符号序列排序存在一些有趣的规律 .对耦合格子映射研究、非线性耦合则量等是非常有启发意义的 .

To recover the initial signals in coupled map lattices (CMLs) is a key work when CMLs are applied to signal processing. In this paper, a method to roughly recover the initial signal is proposed. Numerical simulations show that the mean of recovered initial conditions from the coupled map lattices is equal to that of the given(real value) and the variance of recovered initial conditions is less than that of the given. For explaining these properties, when a Logistic map is coupled to others, it is taben as undergoing a transformation. Meanwhile, some interesting phenomena are found to sort two sequences obtained under Logistic mapping with different parameters. The results in this paper is heuristic for CMLs study and coupled nonlinear measurement etc.