Open AccessEmergence of partial locking states from the ensemble of Winfree oscillators
Author(s) -
SeungYeal Ha,
Dongnam Ko,
Jinyeong Park,
Sang Woo Ryoo
Publication year - 2016
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1448
Subject(s) - synchronization (alternating current) , nonlinear system , coupling (piping) , coupling strength , phase locking , statistical physics , phase (matter) , state (computer science) , phase synchronization , conservation law , nonlinear dynamical systems , mathematics , physics , topology (electrical circuits) , mathematical analysis , quantum mechanics , combinatorics , algorithm , condensed matter physics , materials science , metallurgy
We study the emergence of partial locking states for a subsystem whose dynamics is governed by the Winfree model. The Winfree model is the first mathematical model for synchronization. Thanks to the lack of conservation laws except for the number of oscillators, it exhibits diverse asymptotic nonlinear patterns such as partial and complete phase locking, partial and complete oscillator death, and incoherent states. In this paper, we present two sufficient frameworks for a majority sub-ensemble to evolve to the phase-locked state asymptotically. Our sufficient frameworks are characterized in terms of the mass ratio of the subsystem compared to the total system, ratio of the coupling strength to the natural frequencies, and the phase diameter of the subsystem. We also provide several numerical simulations and compare their results to the analytical results.