ACDC Seminar by Hiroya Nakao on June 23

On the 23th of June at 16.00, Hiroya Nakao (Institute of Science Tokyo, Japan) will give an Amsterdam Dynamics Seminar. We will go for drinks at Bar Boele after the talk.

The talk will take place in the Maryam seminar room (9A-46).

Title: Phase-amplitude coordinates and global phase synchronization decoupled from amplitude dynamics

Abstract: The recent introduction of the Koopman operator framework has provided new insights into the analysis and control of nonlinear dynamical systems. For limit-cycle oscillators, the two principal Koopman eigenfunctions can be used to define phase and amplitude coordinates that globally linearize the dynamics within the basin of attraction. This approach provides an alternative formulation of the classical phase-reduction method based on the notion of asymptotic phase, and further generalizes it to a phase-amplitude reduction method. In this talk, starting with a brief review of phase-amplitude reduction theory for weakly perturbed limit-cycle oscillators, a method is proposed to construct a coupled-oscillator model whose phase and amplitude dynamics are completely decoupled over the entire basin of attraction. It is demonstrated that such a model can achieve global phase synchronization while simultaneously exhibiting arbitrarily complex amplitude dynamics, yielding seemingly counterintuitive synchronization phenomena.

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