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Reshaping-Induced Chaotic Escape from a Potential Well

The chaotic escape of a damped oscillator excited by a periodic string of symmetric pulses of finite width and amplitude from a cubic potential well that typically models a metastable system close to a fold is investigated. Analytical (Melnikov analysis) and numerical results show that chaotic escapes are typically induced over a wide range of parameters by hump-doubling of an external excitation which is initially formed by a periodic string of single-humped symmetric pulses. The analysis reveals that the threshold amplitude for chaotic escape 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. We discuss a physical mechanism concerning the impulse transmitted by the pulse which explains the aforementioned results.