Synchronization and peak-to-peak dynamics in networks of low-dimensional chaotic oscillators

In this paper we study the relationships between local and global properties in networks of dynamical systems by focusing on two global properties, synchronization and peak-to-peak dynamics, and on two local properties, coherence of the components of the network and coupling strength. The analysis is restricted to networks of low-dimensional chaotic oscillators, i.e. oscillators which have peak-to-peak dynamics when they work in isolation. The results are obtained through simulation first by considering pairs of coupled Lorenz, Rossler and Chua systems, and then by studying the behavior of spatially extended tritrophic food chains described by the Rosenzweig-MacArthur model. The conclusion is that synchronization and peak-to-peak dynamics Lire different aspects of the same collective behavior. which is easily obtained by enhancing local coupling and coherence. The importance of these findings is briefly discussed within the context of ecological modeling.