Entropy test for complexity in chaotic time series

Abstract

We perform an entropy test, combined with a diagnostic test for the degree of visible determinism, for the complexity in chaotic time series. A time series is coarse-grained into a binary sequence, partitioned into segments of D binary digits, and transformed into a string of “alphabets” binary-coded in D bits. Using the probability density function estimated from the histogram representing the frequencies of appearance of the 2^D alphabets in the string, we calculate the information entropy referred to as the string entropy. Case studies are conducted for numerical time series generated by the logistic map, the tent map, the Lorenz equations, and the augmented Lorenz equations. We discuss the performances of the time series as sequences of pseudorandom numbers for chaotic cryptography.