Abstract: This paper analyzes different methods for determining delay time in state space reconstruction. Although the method of mutual information is more accurate, its computational process is quite cumbersome and time-consuming. So based on the pseudo-periodicity of chaotic attractor, it puts forward a new algorithm to refine delay time step by step using mutual information. The numerical experiment of R?ssler and Lorenz systems proves the reliability of this algorithm.

Key words: state space reconstruction, time series, delay time, mutual information, pseudo-periodicity

摘要： 对比研究混沌时间序列相空间重构中对延迟时间选取的各种算法，根据混沌吸引子所具有的伪周期性与各态历经的性质，提出采用逐步细化的方法寻找系统互信息函数的第一局部最小值，作为最佳的延迟时间。克服了传统互信息函数计算繁琐、难以编程实现的缺点，兼具精确性与高效性。通过R?ssler和Lorenz系统的数值仿真结果验证了算法的可靠性。

关键词: 相空间重构, 时间序列, 延迟时间, 互信息, 伪周期性