Averaging of noisy nonlinear systems with rapidly oscillating and decaying components

N. Sri Namachchivaya, Henry J. Van Roessel

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

Original languageEnglish (US)
Pages (from-to)329-347
Number of pages19
JournalNonlinear Dynamics
Volume36
Issue number2-4
DOIs
StatePublished - Jun 2004

Keywords

  • Bifurcation
  • Martingale problem
  • Stochastic averaging
  • Weak convergence

ASJC Scopus subject areas

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

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