Abstract: Both the periods of chaotic sequences when iterating on computer and their distribution based on floating point formats have been studied in this paper. By constructing nonstandard floating point formats matched with the IEEE standard ones, the periods of six common chaotic systems under different floating point precisions were measured. Using a linear fitting method, the distribution relationship between the periods of chaotic sequence and numerical precisions was obtained, which corrected the distribution relationship based on fixed point formats and gave an experimental criterion for the study of chaotic antidegradation. This paper also shows that for the chaotic sequence, conclusions based on fixed point formats can not be simply extended to floating point formats.

Key words: chaos, floating point, finite-precision effect, period

摘要： 研究了计算机迭代下基于浮点格式的混沌序列周期及其分布规律。通过构造与标准浮点格式匹配的非标准浮点格式，统计测算了六种常见混沌系统在不同浮点精度下退化的混沌序列周期及其分布，采用线性拟合方法获得了混沌序列周期随计算精度变化的分布关系，纠正了多年来基于定点格式的相应分布关系，为后续的混沌抗退化机制研究提供了一个合理的可用于实验测试的参考标准，也表明对于混沌序列而言，基于定点格式的结论不能简单随意推广到浮点格式。

关键词: 混沌, 浮点, 有限精度效应, 周期