Transient chaos in a parametrically damped pendulum

Abstract

The parametrically damped pendulum exhibits chaotic transients over a sizable portion of its state space. Using the techniques of interpolated cell mapping (ICM), it has been found that these transients arise from the spatial congruence of the basin of attraction of a stable stationary solution and the remnant of a destroyed strange attractor. The mean transient lifetime is found to scale as \ensuremath{\Vert}\ensuremath{\epsilon}-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{c}}$${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$, where \ensuremath{\epsilon} is a system control parameter, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{c}}$ is its value at the chaotic boundary, and \ensuremath{\gamma} is the critical exponent. Also included are ICM data that reveal the nature of basin transformations as nonchaotic boundaries in the state diagram are traversed.