The asymptotic stability of a noisy non-linear oscillator

L. Arnold, P. Imkeller, N. Sri Namachchivaya

Research output: Contribution to journalArticlepeer-review


The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers oscillator driven by either a multiplicative or an additive white-noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity √ε and dissipation ε the exponent grows in proportion with ε1/3.

Original languageEnglish (US)
Pages (from-to)1003-1029
Number of pages27
JournalJournal of Sound and Vibration
Issue number3-5
StatePublished - Jan 22 2004

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


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