Pinning of reaction–diffusion travelling waves in one-dimensional annular geometry

We analyse the complex dynamics arising in a one-dimensional bistable advection–reaction–diffusion equation on a bounded annular domain, along with its simplest nontrivial approximation in terms of a Fourier expansion. We investigate the pinning of travelling waves produced by spatial anisotropies and suggest possible biological implications in the context of cardiac action potential propagation failure due to acute ischemia. • Travelling nonlinear waves play a prominent role in biological systems. • We study the propagation of nonlinear waves a bounded domain. • The effects of reflection and translational symmetry breaking are analysed. • The pinning of travelling waves is studied using equivariant bifurcation theory.