Abstract

A unified framework for the study of stability of solutions to delay differential equations perturbed deterministically and stochastically has been presented. We review the concepts of Hopf bifurcation, centre manifold, integral averaging method and pth–moment Lyapunov exponent, and then demonstrate their role in the stability study of a modified Duffing oscillator with time delay. Sufficient conditions ensuring Đ- and Þ–bifurcations and the changes in character of the probability density function are established for fixed and positive time delay.

Volume Subject Area:
18th Biennial Conference on Mechanical Vibration and Noise
Keywords:
Moment Lyapunov exponent, time delay, Hopf bifurcation, centre manifold, deterministic and stochastic stability
Topics:
Bifurcation, Delays, Equilibrium (Physics), Manifolds, Stability
This content is only available via PDF.
Copyright © 2001 by ASME
You do not currently have access to this content.