We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh--Nagumo model. First, we derive the profile of 1-pulse undetermined width and propagating speed. Next, compute associated for this from which conditions existence saddle-node bifurcation as zeros its derivatives. obtain same by using diff...

In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which called reaction–interface systems. All weak entire solutions originating finitely many excited intervals completely characterized. For infinitely intervals, periodic wave trains and time-periodic discussed. In particular, we study dispersion rel...

We present numerical evidence that, in the presence of a suitable electric field, an isolated broken plane wave retracting originally in subexcitable media can propagate continuously and eventually evolve into a rotating spiral. Simulations for the FitzHugh-Nagumo, the Barkley, and the Oregonator models are carried out and the same electric-field-sustained spiral phenomena are observed. Semiana...

Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely ...