Strange nonchaotic attractors of the damped pendulum with quasiperiodic forcing.

Abstract

We discuss the existence and properties of strange nonchaotic attractors for the damped pendulum equation with two-frequency quasiperiodic forcing. In particular we present evidence that the equation does indeed exhibit strange nonchaotic attractors and that these attractors are typical (in the sense that they exist on a (Cantor) set of positive Lebesgue measure in parameter space). We also show that the strange nonchaotic attractors have distinctive frequency power spectral characteristics which may make them observable in experiments involving physical nonlinear phenomena which can be modeled by the damped-forced-pendulum equation (e.g., Josephson junctions and sliding charge-density waves). Finally the transition to chaotic behavior is illustrated.