Random perturbations of a periodically driven nonlinear oscillator: Escape from a resonance zone

Nishanth Lingala, N. Sri Namachchivaya, Ilya Pavlyukevich

Research output: Contribution to journalArticlepeer-review

Abstract

For nonlinear oscillators, frequency of oscillations depends on the oscillation amplitude. When a nonlinear oscillator is periodically driven, the phase space consists of many resonance zones where the oscillator frequency and the driving frequency are commensurable. It is well known that, a small subset of initial conditions can lead to capture in one of the resonance zones. In this paper we study the effect of weak noise on the escape from a resonance zone. Using averaging techniques we obtain the mean exit time from a resonance zone and study the dependence of the exit rate on the parameters of the oscillator.

Original languageEnglish (US)
Pages (from-to)1376-1404
Number of pages29
JournalNonlinearity
Volume30
Issue number4
DOIs
StatePublished - Feb 22 2017

Keywords

  • averaging
  • mean exit time
  • resonance

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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