A global well-posedness and asymptotic dynamics of the kinetic winfree equation

Seung Yeal Ha, Jinyeong Park, Xiongtao Zhang

Research output: Contribution to journalArticle


We study a global well-posedness and asymptotic dynamics of measure-valued solutions to the kinetic Winfree equation. For this, we introduce a second-order extension of the first-order Winfree model on an extended phase-frequency space. We present the uniform(-in-time) `p-stability estimate with respect to initial data and the equivalence relation between the original Winfree model and its second-order extension. For this extended model, we present uniform-in-time mean-field limit and large-time behavior of measure-valued solution for the second-order Winfree model. Using stability and asymptotic estimates for the extended model and the equivalence relation, we recover the uniform mean-field limit and large-time asymptotics for the Winfree model. 200 words.

Original languageEnglish
Pages (from-to)1317-1344
Number of pages28
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number4
StatePublished - 2020 Jan 1



  • Asymptotic behavior
  • Mean-field limit
  • Measure-valued solution
  • Synchronization
  • The Winfree model

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