0
RESEARCH PAPERS

Hopf Bifurcation in the Presence of Both Parametric and External Stochastic Excitations

[+] Author and Article Information
N. Sri Namachchivaya

Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, Ill. 61801

J. Appl. Mech 55(4), 923-930 (Dec 01, 1988) (8 pages) doi:10.1115/1.3173743 History: Received September 09, 1986; Revised April 23, 1988; Online July 21, 2009

Abstract

In this paper the effect of small parametric and external stochastic perturbations on a two-dimensional system exhibiting Hopf bifurcation is discussed in detail. It is shown that even small fluctuations in parameters can have an important effect when the system is in the neighborhood of bifurcation points. The Markov diffusion approximation is used to obtain analytical results relating to the statistical properties of the stochastic response. Both moment and sample stability conditions along with the stationary moments are obtained. For the nonlinear system, stationary and transient probability densities are found along with their stationary moments. It was found that in nonlinear systems, a shift of the bifurcation point takes place due to the presence of parametric noise.

Copyright © 1988 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In