Abstract
The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ε and dissipation ε2 the exponent grows in proportion with ε2/3.
Original language | English (US) |
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Pages (from-to) | 143-165 |
Number of pages | 23 |
Journal | Nonlinear Dynamics |
Volume | 47 |
Issue number | 1-3 |
DOIs | |
State | Published - Jan 2007 |
Keywords
- Hamiltonian
- Markov processes
- Martingale problem
- Stochastic averaging
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Ocean Engineering
- Mechanical Engineering
- Applied Mathematics
- Electrical and Electronic Engineering