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RESEARCH PAPERS

Co-dimension Two Bifurcations in the Presence of Noise

[+] Author and Article Information
N. Sri Namachchivaya

Aeronautical and Astronautical Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2997

J. Appl. Mech 58(1), 259-265 (Mar 01, 1991) (7 pages) doi:10.1115/1.2897161 History: Received March 31, 1989; Revised November 16, 1989; Online March 31, 2008

Abstract

Some results pertaining to co-dimension two stochastic bifurcations are presented. The normal form associated with non-semi-simple double-zero eigenvalues is considered. The method of stochastic averaging applicable for singularly perturbed stochastic differential equations is used to further reduce the problem to a one dimensional diffusion process. Probability density, most probable values, stability conditions in probability, and mean exit times are obtained for the reduced system.

Copyright © 1991 by The American Society of Mechanical Engineers
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