Dynamical patterns in scalefree trees of coupled 2D chaotic maps

Abstract

New insights have been gained recently into the interplay between complex network architectures and the collective dynamics of simple elements coupled through them. The usual paradigm for studying systems of this kind is a network of one-dimensional interacting logistic maps, which provides a plausible model for a variety of complex systems. In this work we consider a network of two-dimensional standard maps coupled through a scalefree tree topology. The coupling is solely in the angle coordinate and involves a time-delay: this approach is motivated by the node-to-node information flow view of the collective dynamics. We observe a rich variety of dynamical behavior including self-organized patterns: nodes synchronize in clusters each having specific motion quantities whose values are belonging to a discrete set of possible values. We conclude by studying the relationship between dynamically induced cluster-organization of the nodes and their network-structurization. © Springer-Verlag Berlin Heidelberg 2007.