Controlling Chaos: The Example of an Impact Oscillator

Abstract

The OGY algorithm (Ott et al., 1990) allows the conversion of a chaotic attractor to any one of a large number of periodic orbits by making small time-dependent perturbations of an available system parameter. We have applied this method to impact oscillators and stabilized its chaotic attractor on period-1 and period-2 orbits using small time-dependent pertubations of the driving frequency. We also demonstrate the ability to switch the chaotic system between the period-1 and period-2 orbits at will by controlled time-dependent perturbations. However, before the system settles on the stabilized orbit, it exhibits a long chaotic transient. We demonstrate how the exponential sensitivity of a chaotic system to small perturbations can be exploited to control the duration of this chaotic transient.