Bifurcation of traveling waves in extrinsic semiconductors

We analyze the bifurcation of traveling waves in a standard model of electrical conduction in extrinsic semiconductors. In scaled variables the corresponding traveling wave problem is a singularly perturbed nonlinear three-dimensional o.d.e. system. The relevant bifurcation parameters are the wave speed s and the total current j. By means of geometric singular perturbation theory it suffices to analyze a two-dimensional reduced problem. Depending on the relative size of s and a dimensionless small parameter β different types of traveling waves exist. For 0≤s≪β the only waves are fronts corresponding to heteroclinic orbits. For β≪s similar fronts — but with left and right states reversed — exist. The transition between these regimes occurs for s=O(β) in a complicated global bifurcation involving a Hopf bifurcation, bifurcation of multiple periodic orbits, and heteroclinic and homoclinic bifurcations. We present a consistent bifurcation diagram which is confirmed by numerical computations.