Cooperative dynamics in coupled systems of fast and slow phase oscillators

Hidetsugu Sakaguchi, Takayuki Okita

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    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.

    Original languageEnglish
    Article number022212
    JournalPhysical Review E
    Volume93
    Issue number2
    DOIs
    Publication statusPublished - Feb 16 2016

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

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