Bifurcation of traveling waves in extrinsic semiconductors

We analyze the bifurcation of traveling waves in a standard model of electr ical conduction in extrinsic semiconductors. In scaled variables the corres ponding traveling wave problem is a singularly perturbed nonlinear three-di mensional o.d.e. system. The relevant bifurcation parameters are the wave s peed 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 beta differe nt types of traveling waves exist. For 0 less than or equal to s much less than beta the only waves are fronts corresponding to heteroclinic orbits. F or beta much less than s similar fronts - but with left and right states re versed - exist. The transition between these regimes occurs for s = O(beta) in a complicated global bifurcation involving a Hopf bifurcation, bifurcat ion of multiple periodic orbits, and heteroclinic and homoclinic bifurcatio ns. We present a consistent bifurcation diagram which is confirmed by numer ical computations. (C) 2000 Elsevier Science B.V. All rights reserved.