Non-standard reduction of noisy duffing-van der Pol equation

N. Sri Namachchivaya, Richard B. Sowers, Lalit Vedula

Research output: Contribution to journalArticle

Abstract

The purpose of this work is to improve the understanding of the solution of the noisy Duffing-van der Pol equation. We achieve this by developing rigorous methods to replace, in some limiting regime, the original complicated system by a 'simpler, constructive, and rational' approximation - a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional Hamiltonian system. We achieve the model-reduction through 'stochastic averaging' and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results, namely, mean exit times, probability density functions, and stochastic bifurcations.

Original languageEnglish (US)
Pages (from-to)223-245
Number of pages23
JournalDynamical Systems
Volume16
Issue number3
DOIs
StatePublished - Sep 2001

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Non-standard reduction of noisy duffing-van der Pol equation'. Together they form a unique fingerprint.

  • Cite this