Metamorphoses of Basin Boundaries in Nonlinear Dynamical Systems

A basin boundary can undergo sudden changes in its character as a system parameter passes through certain critical values. In particular, basin boundaries can suddenly jump in position and can change from being smooth to being fractal. We describe these changes ("metamorphoses") and find that they involve certain special unstable orbits on the basin boundary which are accessible from inside one of the basins. The forced damped pendulum (Josephson junction) is used to illustrate these phenomena.