Linear response theory for coupled phase oscillators with general coupling functions. (7th January 2020)

• Record Type: Journal Article
• Authors: Terada, Yu; Yamaguchi, Yoshiyuki Y
• Is Part Of: Journal of physics. Volume 53:Number 4(2020)
• Publication Date: 2020-01-07
• Subjects: synchronization -- linear response theory -- coupled oscillators; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab5eaf
• Languages: English
• ISSNs: 1751-8113

Abstract

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 phase-lag parameters, and any values for the time-delay parameter. This generality is in contrast to the limitation of the previous methods of the Ott–Antonsen ansatz and the self-consistent 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.