Invariant Measure and Lyapunov Exponents for two Dimensional Parametrically Excited Random Systems
Rong Haiwu  Xu Wei  Fang Tong
(Northwestern Polytechnical University, Xi'an 710072)

Abstract: For the stability investigation of linear systems with parameter fluctuations we follow Khasminskii's
concept to separate a stationary solution part by introducing polar coordinates. In the two-dimensional case
this projection lives on the unit circle and determines the associated invariant measures and Lyapunov
exponents according to Oseledec's multiplicative ergodic theorem. Results are obtained for parametric excitation by broad-band and narrow-band random processes,both cases are covered by a generalized
fluctuation model.
Keywords: parametrically excited random systems, invariant measure, top Lyapunov exponent, broad-band noise, narrow-band noise.