Controlling escape from a potential well by reshaping periodic secondary excitations

The role of the wave form of periodic secondary excitations at controlling (suppressing and enhancing) escape from a potential well is investigated. We demonstrate analytically (by Melnikov analysis) and numerically that a judicious choice of the excitation's wave form greatly improves the effectiveness of the escape-controlling excitations while keeping their amplitude and period fixed. These predictions are confirmed by an energy-based analysis that provides the same optimal values of the escape-controlling parameters. The example of a dissipative Helmholtz oscillator is used to illustrate the accuracy of these results.