title: Cooperative dynamics in coupled systems of fast and slow phase oscillators.
abstract: We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasiperiodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is derived using the Ott-Antonsen ansatz. The applicability of the ansatz is checked by the comparison of numerical results of the coupled oscillator system and the reduced low-dimensional equation. We investigate further several interesting phenomena in which mutual interactions between the fast and slow oscillators play an essential role. Fast oscillations appear intermittently as a result of excitatory interactions with slow oscillators in a certain parameter range. Slow oscillators experience an oscillator-death phenomenon owing to their interaction with fast oscillators. This oscillator death is explained as a result of saddle-node bifurcation in a simple phase equation obtained using the temporal average of the fast oscillations. Finally, we show macroscopic synchronization of the order 1:m between the slow and fast oscillators.
authors.affiliation: Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
authors.forename: Hidetsugu
authors.initials: H
authors.lastname: Sakaguchi
authors.affiliation: Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
authors.forename: Takayuki
authors.initials: T
authors.lastname: Okita
mesh_terms: D017711:Nonlinear Dynamics