제목: Emergent behaviors of infinite Winfree oscillators
일시: 2026년 2월 11일 (수) 오전 11:00 - 오후 12:00
장소: 자연과학관 744호
연사: 이승준 (서울대학교)
초록:
In this talk, we investigate the emergent behaviors of infinite Winfree oscillators. Synchronization phenomena, where coupled oscillators adjust their rhythms through weak couplings, are pervasive in nature, and they have been actively studied since the pioneering works of Winfree and Kuramoto. We analyze the infinite Winfree model in three settings: continuous-time dynamics over a countable set of oscillators, its discrete-time analogue via the first-order Euler scheme, and the continuum model described by an integro-differential equation. For each framework, we rigorously establish sufficient conditions for the emergence of asymptotic patterns such as boundedness, stability and phase-locking. In particular, we show the uniform-in-time convergence of the discrete dynamics to the continuous one and the continuum limit.
일시: 2026년 2월 11일 (수) 오전 11:00 - 오후 12:00
장소: 자연과학관 744호
연사: 이승준 (서울대학교)
초록:
In this talk, we investigate the emergent behaviors of infinite Winfree oscillators. Synchronization phenomena, where coupled oscillators adjust their rhythms through weak couplings, are pervasive in nature, and they have been actively studied since the pioneering works of Winfree and Kuramoto. We analyze the infinite Winfree model in three settings: continuous-time dynamics over a countable set of oscillators, its discrete-time analogue via the first-order Euler scheme, and the continuum model described by an integro-differential equation. For each framework, we rigorously establish sufficient conditions for the emergence of asymptotic patterns such as boundedness, stability and phase-locking. In particular, we show the uniform-in-time convergence of the discrete dynamics to the continuous one and the continuum limit.