Linked e-resources
Details
Table of 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.
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.