Synchronous behaviors of oscillatory complex systems are ubiquitous in many biological and chemical systems, to name a few, firing of fireflies, synchronization of metronomes, rhythmic beating of pacemaker cells, etc.
Famous examples are the Kuramoto model, which is a phase-coupled model, and the Winfree model, which is a pulse-coupled model.
Both ode systems describe the time-evolutionary behavior of oscillators on one dimensional torus.
Continuum and mean-field limit is an effective approximation to describe a system with infinitely many particles.
In this talk, we first study some examples of the particle models.
Then, we apply time-evolutionary behavior of the particle models to analyze the continuum and kinetic equations obtained as a suitable limit of the particle systems.
Romain Duboscq, Ariane Trescases