Logistic映射的有限字长研究

Finite Word Length Study of Logistic Map

借助计算机对混沌序列进行数值分析必须考虑计算机的存储字长有限这个条件。针对Logistic映射,研究了计算机字长对其混沌特性的影响,由于计算机的字长效应,混沌序列经过短暂的过渡态后演化为周期序列,使用小数据量法计算了处于过渡态和周期态的有限字长混沌序列的最大Lyapunov指数。通过数值计算结果表明:有限字长混沌序列的周期态和过渡态都具有正的最大Lyapunov指数,且小数据量法对有限字长效应是鲁棒的。最后,给出了一个加长有限字长混沌序列演化周期和过渡期的耦合方法。

To analyse the chaotic time sequences by computer should consider the finite word length of the computer. As to the logistic map, this paper studies the effect of finite word length to its chaotic characters. Due to the finite word length of computer, the chaotic sequences will turn into periodic ones after short interim. The maximum Lyapunov exponents are calculated by the small data sets method. The results show that both periodic and transitional chaotic sequences have positive maximum Lyapunov exponent, and the small data sets method is robust to the finite word length of the computer. In the end, a coupled method to improve the period and interim length of chaotic sequences is given.