Main description:

Theformationofcollective behaviorinlargeensemblesornetworksofcoupled oscillatory elements is one of the oldest problem in the study of dyna- cal systems. Nevertheless, it is an actually challenging ?eld for a theoretical understanding as well as for applications in various disciplines, ranging from physics, chemistry, earth sciences via biology and neuroscience to engineering, business and social sciences. Due to the large number of e?ective degrees of freedominspatiallyextendedsystems,arichvarietyofspatiotemporalregimes is observed. Three main types of collective behavior are distinguished (1) a fully incoherent state or highly developed spatiotemporal disorder; (2) p- tially coherent states, where some of the participants in the network behave in some common rhythm, forming clusters; (3) a fully coherent state or a regime of globally synchronized elements. The basic phenomenon of these structure formations is synchronization, i. e. regime of coherent activity, which is u- versal in many dynamical systems and can be understood from the analysis of common models of oscillatory networks. Cooperative phenomena in ensembles of globally (mean-?eld) coupled phase equations were studied ?rst by Winfree and Kuramoto. They showed that if the coupling is strong enough mutual synchronization emerges. In contrast to the mean-?eld Winfree and Kuramoto models, Ermentrout and Kopell’s classic works deal with chains of phase equations. Besides cluster and global synchronization e?ects, the main results there involve travelling waves. A main part of this book presents di?erent aspects of synchronization in chains and lattices of locally interconnected nonidentical nonlinear oscil- tory elements.

Feature:

First monograph on this topic

Written by internationally known exerts in the field

Back cover:

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.

Contents:

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.