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

Nishanth Lingala; Navaratnam Sri Namachchivaya; Ilya Pavlyukevich

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

Probability 2017-02-17 v2 Dynamical Systems

Authors: Nishanth Lingala , Navaratnam Sri Namachchivaya , Ilya Pavlyukevich

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.

Keywords

random perturbations nonlinear oscillator periodic driving resonance zone escape problem weak noise small parameter

Cite

@article{arxiv.1510.08919,
  title  = {Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone},
  author = {Nishanth Lingala and Navaratnam Sri Namachchivaya and Ilya Pavlyukevich},
  journal= {arXiv preprint arXiv:1510.08919},
  year   = {2017}
}

Comments

Presented at IUTAM symposium on analytical methods in nonlinear dynamics, Darmstadt, 6-9 July 2015

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

Abstract

Keywords

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