Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors

We study a simple mechanical system consisting of two rotors that possesses a large number (3000+) of coexisting periodic attractors. A complex fractal boundary separates these tiny islands of stability and their basins of attraction. Hence, the system's long term behavior is acutely sensitive to the initial conditions. This sensitivity combined with the system's many periodic sinks give rise to a rich dynamical behavior when the system is subjected to small amplitude noise. This dynamical behavior is of great utility, and this is demonstrated by using perturbations which are smaller than the noise level to gear and influence the dynamics toward a specific periodic behavior. (C) 1998 Elsevier Science Ltd. All rights reserved.