RESHAPING-INDUCED CONTROL OF CHAOS AND CRISIS PHENOMENA IN A DAMPED, PARAMETRICALLY DRIVEN PENDULUM
The behavior of a damped pendulum parametrically excited by a periodic string of symmetric pulses of finite width and amplitude is investigated. Analytical (Melnikov method) and numerical (bifurcation diagrams) results show that chaos and crises are reliably controlled over a wide range of parameters by hump-doubling of a parametric excitation which is initially formed by a periodic string of single-humped symmetric pulses. In particular, the analysis reveals that the chaotic threshold amplitude when altering solely the pulse shape presents a minimum as a single-humped pulse transforms into a double-humped pulse, the remaining parameters being held constant. Additionally, the mechanism underlying the hump-doubling-induced crises is discussed with the help of a two-dimensional map.