The formation of collective behavior in large ensembles or networks of coupled oscillatory elements is one of the oldest and most fundamental aspects of dynamical systems theory. Potential and present applications span a vast spectrum of fields ranging from physics, chemistry, geoscience, through life- and neurosciences to engineering, the economic and the social sciences. This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or the heart muscle - to name but a few. This book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.

"The formation of collective behavior in large ensembles or networks of coupled oscillatory elements is one of the oldest and most fundamental aspects of dynamical systems theory. Potential and present applications span a vast spectrum of fields ranging from physics, chemistry, geoscience, through life- and neurosciences to engineering, the economic and the social sciences. This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or the heart muscle - to name but a few. This book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models. TOC:Introduction.- Basic Models.- Synchronization Due to External Periodic Forcing.- Synchronization of Two Coupled Systems.- Synchronization in Ensembles of Phase Oscillators.- Synchronization in Chains of Coupled Limit-Cycle Oscillators.- Phase Synchronization in Ensembles of Chaotic OscillatorsWith a Period-Doubling Route to Chaos. Rössler Oscillators.- Synchronization of Intermittent-Like Oscillations in Chains of Coupled Maps.- Regular and Chaotic Phase Synchronisation of Coupled Circle Maps.- Controlling Phase Synchronization in Oscillatory Networks.- Synchronization Structures in Coupled Chains of Limit-Cycle Oscillators.- Synchronization-Like Phenomena in Chains and Lattices of Excitable Luo-Rudy Systems.- Noise-Induced Synchronization and Synchronization-Like Phenomena in Ensembles of Oscillatory and Excitable Systems.- Synchronization in Networks With Complex Topology."

Basics on Synchronization and Paradigmatic Models.- Basic Models.- Synchronization Due to External Periodic Forcing.- Synchronization of Two Coupled Systems.- Synchronization in Geometrically Regular Ensembles.- Ensembles of Phase Oscillators.- Chains of Coupled Limit-Cycle Oscillators.- Ensembles of Chaotic Oscillators with a Periodic-Doubling Route to Chaos, R#x00F6;ssler Oscillators.- Intermittent-Like Oscillations in Chains of Coupled Maps.- Regular and Chaotic Phase Synchronization of Coupled Circle Maps.- Controlling Phase Synchronization in Oscillatory Networks.- Chains of Limit-Cycle Oscillators.- Chains and Lattices of Excitable Luo-Rudy Systems.- Synchronization in Complex Networks and Influence of Noise.- Noise-Induced Synchronization in Ensembles of Oscillatory and Excitable Systems.- Networks with Complex Topology.