Robustness of Nonlinear Systems Perturbed by External Random Excitation

The effect of external random excitation on nonlinear continuous time systems is examined using the concept of the Lyapunov exponent. The Lyapunov exponent may be regarded as the nonlinear/stochastic analog of the poles of a linear deterministic system. It is shown that while the stationary probability density function of the response undergoes qualitative changes (bifurcations) as system parameters are varied, these bifurcations are not reflected by changes in the sign of the Lyapunov exponent. This finding does not support recent proposals that the Lyapunov exponent be used as a basis for a rigorous theory of stochastic bifurcation.