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 LimitCycle 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 FokkerPlanck Equation; 1.7 Some Results for Noiseless Interacting Oscillators; 1.7.1 The Kuramoto Solution; 1.7.2 The OttAntonsen 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 SecondOrder 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 LongRange Interacting System; 3.1.3 Dynamics in a Reduced Parameter Space; 3.2 Nonequilibrium FirstOrder 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 manybody 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 secondorder 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.


Synchronization.


Electronic books. 
ISBN 
9783319966649 (electronic bk.) 

3319966642 (electronic bk.) 

9783319966632 

3319966634 

9783319966656 (print) 

3319966650 
Standard Number 
10.1007/9783319966649 
