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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.
List of contents
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.
Summary
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 even the heart muscle, to name but a few. The 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.
Additional text
From the reviews:
"The book provides a good survey of published (and some unpublished) results on synchronization in networks of coupled oscillators and excitable systems. … The … chapter treats some selected recent results on the impact of complex network topology (e.g., small-world and scale-free networks) on synchronization, which is a topic of great interest that has attracted many researchers in recent years." (Takashi Nishikawa, Mathematical Reviews, Issue 2008 k)
"The book is composed of 14 chapters, with 221 figures and a list of 573 references. … This excellent 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." (A. A. Martynyuk, Zentralblatt MATH, Vol. 1137 (15), 2008)
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From the reviews:
"The book provides a good survey of published (and some unpublished) results on synchronization in networks of coupled oscillators and excitable systems. ... The ... chapter treats some selected recent results on the impact of complex network topology (e.g., small-world and scale-free networks) on synchronization, which is a topic of great interest that has attracted many researchers in recent years." (Takashi Nishikawa, Mathematical Reviews, Issue 2008 k)
"The book is composed of 14 chapters, with 221 figures and a list of 573 references. ... This excellent 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." (A. A. Martynyuk, Zentralblatt MATH, Vol. 1137 (15), 2008)
