A parameter study of epitaxial crystal growth

A third order autonomous ordinary differential equation is studied that is derived from a mathematical model of epitaxial crystal growth on misoriented crystal substrates. The solutions of the ODE correspond to the traveling wave solutions of a nonlinear partial differential equation which is related to the Kuramoto–Sivashinsky equation. The fixed points, the periodic solutions, and the heteroclinic orbits of the ODE are analysed, and stability results are given. A variety of nonlinear phenomena are observed, including Gavrilov–Guckenheimer bifurcations, homoclinic bifurcations, and a cascade of period doublings.