Information theory, synchronization and topological order in complete dynamical networks of discontinuous maps

Abstract

This paper is dedicated to the study of information measures, synchronization and a topological order in complete dynamical networks of discontinuous piecewise linear maps with different slopes. It stands out that the networks topologies are characterized by circulant matrices and the conditional Lyapunov exponents are explicitly determined. Some properties of the mutual information rate and the Kolmogorov–Sinai entropy, depending on the synchronization interval, are discussed. A topological order between the complete dynamical networks is presented, which is characterized by the monotony of the network topological entropy. It is proved that if the network topological entropy increases, then the mutual information rate and the Kolmogorov–Sinai entropy increase or decrease, according to the variation of the coupling parameter. Furthermore, various types of computer simulations show the experimental applications of these results and techniques.