Local entropies as a measure of ordering in discrete maps

Local order measures are applied to a simple dynamical system: the logistic map. The results on pattern entropy are compared with those obtained using other, well-known order measures such as Renyi entropy, Shannon entropy and Lyapunov exponent (an analytical expression). Two modes of calculation are used: the global one and the local one (i.e. calculated in a sliding time window). The properties of local measures are discussed. It is concluded that the local measures defined here may be a natural tool for analysing non-stationary signals.