[MS01] Delay differential equations in mathematical biology and life sciences

[MS01-02] Slow-fast dynamics of delayed FitzHugh-Nagumo model with traveling waves

*Zhengkang Li¹ (1. China University of Mining and Technology (China))

Keywords:

delayed equation,FitzHugh-Nagumo equation,slow-fast dynamics,homoclinic orbit,heteroclinic orbit

This paper investigates a FitzHugh-Nagumo (FHN) model that describes the chemical reactions underlying the dynamics of actin waves in cells. We study traveling pulses in this model, incorporating both doubly-diffusive effects and local time delays. The singular orbits are constructed by analyzing the limiting orbits across three distinct time scales: slow, intermediate, and fast, as derived from the corresponding limiting equations. Finally, the existence of traveling pulses for the full system is established by geometric singular perturbation theory and the Exchange Lemma.