Permutation Entropies and Chaos

Permutation entropy is a metric used to quantify the regularity of a time series. Here I report on its application to the problem of characterizing the behavior of a few nonlinear dynamical systems, specifically the Duffing oscillator and the Tent and Logistic maps. Numerical results indicate that the permutation entropy can in principle be used to detemine the entropy rate of a system, and thus whether it is chaotic or not, but that in practice the convergence is slow. Additionally, comparisons are made between the excess entropy of the tent and logistic maps and a recently defined analagous quantity for permutations, the permutation excess entropy.