Logistic映射的有限字長(zhǎng)研究

借助計(jì)算機(jī)對(duì)混沌序列進(jìn)行數(shù)值分析必須考慮計(jì)算機(jī)的存儲(chǔ)字長(zhǎng)有限這個(gè)條件。針對(duì)Logistic映射，研究了計(jì)算機(jī)字長(zhǎng)對(duì)其混沌特性的影響，由于計(jì)算機(jī)的字長(zhǎng)效應(yīng)，混沌序列經(jīng)過短暫的過渡態(tài)后演化為周期序列，使用小數(shù)據(jù)量法計(jì)算了處于過渡態(tài)和周期態(tài)的有限字長(zhǎng)混沌序列的最大Lyapunov指數(shù)。通過數(shù)值計(jì)算結(jié)果表明：有限字長(zhǎng)混沌序列的周期態(tài)和過渡態(tài)都具有正的最大Lyapunov指數(shù)，且小數(shù)據(jù)量法對(duì)有限字長(zhǎng)效應(yīng)是魯棒的。最后，給出了一個(gè)加長(zhǎng)有限字長(zhǎng)混沌序列演化周期和過渡期的耦合方法。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.