一种非线性分形的时间序列模型表示法

提出了一种基于非线性映射的迭代函数系统（ Ｉ Ｆ Ｓ），并以此作为一个时间序列的模型。为了保证模型成立，文中给出了映射收缩条件并进行了证明。非线性函数以分段函数形式给出，文中讨论了当非线性函数取为多项式形式时模型的求解方法，并对湖底回波进行了实验。实验结果表明，非线性 Ｉ Ｆ Ｓ产生的吸引子能够很好地逼近原信号。

Using Nonlinear Iterated Function System to Model Time Sequences

Linear IFS (Iterated Function System) is simple but the approximation of time sequences is somewhat crude. We propose nonlinear IFS as an alternative; its approximation of time sequences is better but much more complicated than linear IFS. The nonlinear function used is given by eq. (5). For the nonlinear IFS to be dependable in mapping needed for approximating time sequences, the validity of nonlinear IFS must be assured. In section 2.2, we discuss the condition under which this validity is assured. As can be seen from eq. (5), the mapping need to be separately done in three domains. We applied our method to model echoes from a lake bottom. Test data is shown in Fig. 1 and Fig. 2. Comparison of Figs. 1 and 2 shows that very good approximation is attained.