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NUMBER  
AUTHOR Ha, Seung-Yeal
TITLE COLLECTIVE BEHAVIORS OF A WINFREE ENSEMBLE ON AN INFINITE CYLINDER
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JOURNAL DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021
ABSTRACT The Winfree model is the first phase model for synchronization and it exhibits diverse asymptotic patterns that cannot be observed in the Kuramoto model. In this paper, we propose a Winfree type model describing the aggregation of particles on the surface of an infinite cylinder. For a special case, our proposed model is in fact equivalent to the complex Winfree model. For the proposed model, we present a sufficient framework leading to the complete oscillator death and uniform l(p)-stability in a large coupling regime. We also derive the corresponding kinetic model via uniform-in-time mean-field limit. In addition, we also provide several numerical simulations for the particle and compare them with analytical results.
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