LARGEST LYAPUNOV EXPONENTS AND BIFURCATIONS OF STOCHASTIC NONLINEAR-SYSTEMS

Two commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discus sed in light of bifurcation analysis and one expression is selected fo r 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 quantita tively with those evaluated by using the largest Lyapunov exponent of the linearized oscillator. (C) 1996 John Wiley & Sons, Inc.