Inferring global synchrony from local symbolic dynamics

Abstract

Symbolic dynamics based on specific partitions prevents the occurrence of certain symbolic sequences that are characteristics of the dynamical function. Such partitions lead to a maximal difference in the permutation entropy of a chaotic and the corresponding random system. The symbolic dynamics defined by such partition has several practical applications, one of which is the detection of global synchrony in coupled systems. The synchronized state is detected by observing the complete absence or at least low frequency of particular symbol sequences. The method uses short time series and is hence computationally fast. Also, because it compares the symbol sequence of one single unit in the network with some model behavior, it does not depend on the size of the network and is robust against external noise. © Springer-Verlag Berlin Heidelberg 2013.