Chaos in a parametrically damped pendulum

Numerical simulations have shown that a parametrically damped, but otherwise undriven pendulum possesses many of the dynamical modes characteristic of a simple driven pendulum, yet with notable differences. Over most of the parameter space only a stationary steady state is possible. A single domain exists within which are situated three distinct subregions of periodic, multiperiodic, or chaotic motion. The periodic orbits generally occur at half the damping modulation frequency. All of these phenomena have been experimentally observed on an actual pendulum in which parametric damping is generated electronically.