On the bifurcation curve for an elliptic system of FitzHugh-Nagumo type

We study a system of partial differential equations derived from the FitzHugh-Nagumo model. In one dimension solutions are required to satisfy zero Dirichlet boundary conditions on the interval Ω = (−1, 1). Estimates are given to describe bounds on the range of parameters over which solutions exist; numerical computations provide the global bifurcation diagram for families of symmetric and asymmetric solutions. In the two dimensional case we use numerical methods for zero Dirichlet boundary conditions on the square domain Ω = (−1, 1) × (−1, 1). Numerical computations are given both for symmetric and asymmetric, and for stable and unstable solutions.