Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone

Nishanth Lingala; Navaratnam Sri Namachchivaya; Ilya Pavlyukevich

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arXiv · 1510.08919

Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone

Nishanth Lingala·Navaratnam Sri Namachchivaya·Ilya Pavlyukevich

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Abstract

The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that, as $\varepsilon \to 0$, the measure of the set of initial conditions which lead to 'capture in a resonance zone' goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone.

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Nishanth Lingala, Navaratnam Sri Namachchivaya, Ilya Pavlyukevich. 2017-02-16. Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone. https://arxiv.org/abs/1510.08919

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