Collective Dynamics in Infinite Networks of Pulse-Coupled Phase Oscillators

  • Stilianos Louca (Universität Jena)
A3 02 (Seminar room)


This talk will present our work on networks of pulse-coupled phase oscillators in the thermodynamic limit, that is, with the network size tending to infinity. Two models are considered in which oscillators are distributed on a separable metric space, according to a finite Borel measure. The first model is an evolution equation for the oscillator phase field, the second model is a continuity equation in the oscillator phase distribution. Both models are examined with respect to the existence and local stability of synchrony, i.e. all oscillators having one common, time-dependent phase. Continuing, all-to-all pulse-coupled networks of phase oscillators with additive white noise are examined, in the limit where pulses tend to Dirac distributions. This is done using a Fokker-Planck equation for the oscillator phase density. Particular interest is devoted to stationary states (i.e. time-independent phase densities), their existence, uniqueness, stability and bifurcation behaviour at changing noise strength.

11.05.10 19.05.20

Dynamical Systems Seminar

MPI for Mathematics in the Sciences Live Stream

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail