Stability of noisy nonlinear auto-parametric systems

N. Sri Namachchivaya, David Kok, S. T. Ariaratnam

Research output: Contribution to journalArticle

Abstract

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ε and dissipation ε2 the exponent grows in proportion with ε2/3.

Original languageEnglish (US)
Pages (from-to)143-165
Number of pages23
JournalNonlinear Dynamics
Volume47
Issue number1-3
DOIs
StatePublished - Jan 1 2007

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Keywords

  • Hamiltonian
  • Markov processes
  • Martingale problem
  • Stochastic averaging

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Namachchivaya, N. S., Kok, D., & Ariaratnam, S. T. (2007). Stability of noisy nonlinear auto-parametric systems. Nonlinear Dynamics, 47(1-3), 143-165. https://doi.org/10.1007/s11071-006-9063-7