2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session M01: Neurodynamical Models of Cognition
8:00 AM–11:00 AM,
Wednesday, March 8, 2023
Room: Room 124
Sponsoring
Units:
GSNP DSOFT DBIO
Chair: Jason Kim, Cornell University
Abstract: M01.00010 : High-order phase reduction applied to remote synchronization
10:12 AM–10:24 AM
Abstract
Presenter:
Michael Rosenblum
(University of Potsdam, Germany)
Author:
Michael Rosenblum
(University of Potsdam, Germany)
We discuss the analytical and numerical approaches to phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. Particularly, for three coupled Stuart–Landau (SL) oscillators, where the phase can be introduced explicitly, an analytic perturbation procedure yields the explicit second-order approximation [1]. We exploit the analytical result from [1] to analyze the mechanism of the remote synchronization (RS). RS, briefly reported by Okuda and Kuramoto as early as 1991, implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. Previous studies uncovered the role of amplitude dynamics and of nonisochronicity: RS appeared in a network of isochronous SL units but not in its first-order phase approximation, the Kuramoto network. Furthermore, RS emerged in networks of phase oscillators with the Kuramoto-Sakaguchi interaction, but not in the case of zero phase shift in the sine-coupling term; this result indicates the role of nonisochronicity. In this work, we analytically demonstrate the role of two factors promoting remote synchrony. These factors are the nonisochronicity of oscillators and the coupling terms appearing in the second-order phase approximation. We explain the contribution of both factors and quantitatively describe the transition to RS. We demonstrated that the RS transition is determined by the interplay of the nonisochronicity and the amplitude dynamics. The impact of the latter factor renders the standard first-order phase dynamics descripion of the RS phenomenon invalid. Our result emphasizes the importance of higher-order phase reduction and highlights the crucial role amplitude dynamics may have in governing the behavior of networks of nonlinear oscillators. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths and argue that the effect of the amplitude dynamics neglected in the first-order phase approximation and revealed by the higher-order one holds for general limit-cycle oscillators.