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

    Fingerprint

    Coupled System
    oscillators
    Coupled Oscillators
    death
    Interaction
    Oscillation
    Quasi-periodic Motion
    Saddle-node Bifurcation
    oscillations
    Order Parameter
    saddles
    interactions
    direct numerical simulation
    Synchronization
    synchronism
    Numerical Results
    Range of data

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Medicine(all)

    Cite this

    Cooperative dynamics in coupled systems of fast and slow phase oscillators. / Sakaguchi, Hidetsugu; Okita, Takayuki.

    In: Physical Review E, Vol. 93, No. 2, 022212, 16.02.2016.

    Research output: Contribution to journalArticle

    @article{b3cd131783f2451db008445f86b4a4f9,
    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.",
    author = "Hidetsugu Sakaguchi and Takayuki Okita",
    year = "2016",
    month = "2",
    day = "16",
    doi = "10.1103/PhysRevE.93.022212",
    language = "English",
    volume = "93",
    journal = "Physical Review E",
    issn = "2470-0045",
    publisher = "American Physical Society",
    number = "2",

    }

    TY - JOUR

    T1 - Cooperative dynamics in coupled systems of fast and slow phase oscillators

    AU - Sakaguchi, Hidetsugu

    AU - Okita, Takayuki

    PY - 2016/2/16

    Y1 - 2016/2/16

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=84959421959&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84959421959&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevE.93.022212

    DO - 10.1103/PhysRevE.93.022212

    M3 - Article

    C2 - 26986336

    AN - SCOPUS:84959421959

    VL - 93

    JO - Physical Review E

    JF - Physical Review E

    SN - 2470-0045

    IS - 2

    M1 - 022212

    ER -