Related Experiment Video
Updated: Jul 30, 2026

Basic Caenorhabditis elegans Methods: Synchronization and Observation
Published on: June 10, 2012
Chapman-enskog method and synchronization of globally coupled oscillators
1Escuela Politecnica Superior, Universidad Carlos III de Madrid, Avenida Universidad 30, 28911 Leganes, Spain.
Abstract:
The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model that includes "inertial" effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.
Related Concept Videos
Oscillations about an Equilibrium Position
Damped Oscillations
Although friction and other non-conservative...
Forced Oscillations
Oscillations In An LC Circuit
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Time and frequency -Domain Interpretation of Phase-lag Control
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...

