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Shock and Vibration
Volume 3, Issue 4, Pages 313-320

Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems

C.W.S. To and D.M. Li

Department of Mechanical Engineering, University of Western Ontario, London, Ontario N6A 589, Canada

Received 22 January 1995; Accepted 10 January 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discussed in light of bifurcation analysis and one expression is selected for evaluating the largest Lyapunov exponent of a linearized system. An independent method, developed earlier by the authors, is also applied to determine the bifurcation points of a van der Pol oscillator under parametric random excitation. It is shown that the bifurcation points obtained by the independent technique agree qualitatively and quantitatively with those evaluated by using the largest Lyapunov exponent of the linearized oscillator.