Interplay of random inputs and adaptive couplings in the winfree model

Abstract

We study a structural robustness of the complete oscillator death state in the Winfree model with random inputs and adaptive couplings. For this, we present a sufficient framework formulated in terms of initial data, natural frequencies and adaptive coupling strengths. In our proposed frame-work, we derive propagation of infinitesimal variations in random space and asymptotic disappearance of random effects which exhibits the robustness of the complete oscillator death state for the random Winfree model.