Dynamics of Oscillator Populations: Exact Finite-Dimensional Reduction and Beyond

Explore the dynamics of large ensembles of globally coupled oscillators in this 29-minute lecture by Arkady Pikovsky from the PCS Institute for Basic Science. Delve into the kinetic equations describing the evolution of distribution densities for phase-only oscillator models. Discover the Ott-Antonsen invariant manifold and its extension to a three-complex-variable system for arbitrary initial conditions. Examine the equivalence to the Watanabe-Strogatz system in the noise-free case of identical oscillators. Learn how to follow transients to attracting Ott-Antonsen states using a six-dimensional equation system. Investigate approaches beyond Ott-Antonsen theory, including the circular cumulants technique for noisy systems and the transfer matrix method for describing stationary states in oscillator populations with multiharmonic coupling. Gain insights into global coupling, phase equations, dimensional reduction, and the effects of Gaussian noise on oscillator dynamics.