BIFURCATIONS OF AN OPTICALLY PUMPED 3-LEVEL LASER MODEL

We study the bifurcations in a sixth-order model of a resonant, homogeneously broadened, three-level, optically pumped laser. Standard analytical and numerical techniques are used to obtain a complete unfolding of the model's equilibrium bifurcations in its four-dimensional parameter space. Regions of stationary, periodic and potentially chaotic behaviour are then readily identified. Turning to two specific cases, we study the principal global bifurcations in a two-parameter plane and show their origin in special degenerate bifurcation points of codimension two. The different relative dispositions of the principal homoclinic and heteroclinic connections in these two examples result in different local bifurcation behaviours and chaotic dynamics, which we illustrate in detail.