17.07.2023 15:00 Jaeyoung Yoon:
Winfree model with higher-order couplings and influencesOnline: attend (945856)
We introduce Winfree model, which was proposed by Arthur Winfree to describe the collective behavior of pulsatile oscillators. In this talk, we focus on Winfree model with higher-order influences, which is the first attempt to make mathematical analysis for the approximated pulse-coupled model. We study the sufficient conditions for coupling strengths, in terms of order in influence, for death, locking and incoherence. Next, we add randomness on the order in influence. In this case, we mainly consider the complete oscillator death. We prove exponential-relaxation toward equilibrium and provide a local sensitivity in probability space.