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Synchronization and peak-to-peak dynamics in networks of low-dimensional chaotic oscillators. (English) Zbl 1116.37024

Summary: 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, Rössler 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 are 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.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37N99 Applications of dynamical systems
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