Linear response theory for coupled phase oscillators with general coupling functions
Abstract
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is applicable to a wide class of coupled phase oscillator systems and allows for any coupling functions, any natural frequency distributions, any phaselag parameters, and any values for the timedelay parameter. This generality is in contrast to the limitation of the previous methods of the OttAntonsen ansatz and the selfconsistent equation for an order parameter, which are restricted to a model family whose coupling function consists of only a single sinusoidal function. The theory is verified by numerical simulations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2020
 DOI:
 10.1088/17518121/ab5eaf
 arXiv:
 arXiv:1907.10983
 Bibcode:
 2020JPhA...53d4001T
 Keywords:

 synchronization;
 linear response theory;
 coupled oscillators;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Condensed Matter  Statistical Mechanics
 EPrint:
 doi:10.1088/17518121/ab5eaf