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Cover Art
Author Gupta, Shamik, author.

Title Statistical physics of synchronization / Shamik Gupta, Alessandro Campa, Stefano Ruffo.

Published Cham : Springer, 2018.


Location Call No. Status
Physical description 1 online resource.
Series SpringerBriefs in complexity
SpringerBriefs in complexity.
Springer Physics and Astronomy eBooks 2018 English+International
Bibliography Includes bibliographical references.
Contents Intro; Foreword; Preface; Contents; 1 Synchronizing Systems; 1.1 Introduction; 1.2 The Oscillators and Their Interaction: A Qualitative Discussion; 1.3 Oscillators as Limit Cycles; 1.4 Interacting Limit-Cycle Oscillators; 1.5 Synchronizing Systems as Statistical Mechanics Systems; 1.5.1 A Single Oscillator with Noise; 1.5.2 Oscillators in Interaction; 1.6 The Features of a Statistical Physics Description; 1.6.1 The Advantages of the Fokker-Planck Equation; 1.7 Some Results for Noiseless Interacting Oscillators; 1.7.1 The Kuramoto Solution; 1.7.2 The Ott-Antonsen Solution.
Appendix 2: Form of the Function r(K) for Symmetric and Unimodal Frequency Distributions in the Kuramoto ModelAppendix 3: The Numerical Solution of Eq. (2.34); References; 3 Oscillators with Second-Order Dynamics; 3.1 Generalized Kuramoto Model with Inertia and Noise; 3.1.1 Relation to Electrical Power Distribution Networks; 3.1.2 The Model as a Long-Range Interacting System; 3.1.3 Dynamics in a Reduced Parameter Space; 3.2 Nonequilibrium First-Order Synchronization Phase Transition: Simulation Results; 3.3 Analysis in the Continuum Limit: The Kramers Equation.
Summary This book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.
Other author Campa, Alessandro, author.
Ruffo, Stefano, author.
SpringerLink issuing body.
Subject Statistical physics.
Electronic books.
ISBN 9783319966649 (electronic bk.)
3319966642 (electronic bk.)
9783319966656 (print)
Standard Number 10.1007/978-3-319-96664-9