Finite Word Length Study of Logistic Map

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.