Complex Lorenz equations

For the complex Lorenz model, which is one of basic laser models, it is shown that the phase space has the geometric structure associated with a fiber bundle. Using the equation of motion in the base space of the fiber bundle, we find the surfaces bounding the attractors in this space. The homoclinic `butterfly' responsible for the Lorenz-like attractor appearance is shown to correspond to a codimension-two bifurcation.