Traveling pulses of coupled FitzHugh-Nagumo equations with doubly-diffusive effect

This paper considers a kind of coupled FitzHugh-Nagumo (FHN) equations, combined the classical FHN equations with the mechanics equation. The traveling pulses in coupled FHN equations in the presence of doubly-diffusive effect and local time delay are investigated. The singular orbits are constructed by analyzing limit dynamics of the equations in the traveling wave framework. Particularly, the full system involves three time scales, making it more challenging to seek for the invariant manifold. In order to establish the traveling pulses for the full system, the main analysis relies on the geometric singular perturbation theory and Exchange Lemma.