MEASURE-VALUED DEATH STATE AND LOCAL SENSITIVITY ANALYSIS FOR WINFREE MODELS WITH UNCERTAIN HIGH-ORDER COUPLINGS

초록

We study the measure-valued death state and local sensitivity analysis of the Winfree model with uncertain high-order couplings and its mean-field counterpart. The Winfree model is the first mathematical model for synchronization, and it can be cast as the effective approximation of the pulse-coupled model for synchronization, and it exhibits diverse asymptotic patterns depending on system parameters and initial data. For the proposed models, we present several frameworks leading to oscillator death in terms of system parameters and initial data, and the propagation of regularity in random space. We also present several numerical tests and compare them with analytical results.

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