- Author
- Frey, M. R. | Simiu, E.
- Title
- Noise-Induced Chaos and Phase Space Flux: A Sample-Theoretic Study.
- Coporate
- National Institute of Standards and Technology, Gaithersburg, MD
- Sponsor
- Minerals Management Service, Reston, VA
- Report
- NISTIR 4791, March 1992, 36 p.
- Distribution
- Available from National Technical Information Service
- Keywords
- noise (sound) | chaos | space flux | global perturbation methods | homoclinic orbit | asymptotic mean stationarity | sample-theoretic method
- Abstract
- We study the effect of additive noise on near-integrable second-order dynmaical systems whose unperturbed flows have homoxlinic or heteroclinic orbits. The noise is represented by a type of Shinozuka stochastic process capable of artitrarily closely approximating Gaussian noise with any specified spectrum. We derive a formula for the flux factor applicable for any asymptotic mean stationary excitation. This derivation shows that, to first order, the effect of the external excitation on the system is mediated by a linear filter associated with the system homocolinic or heteroclinic orbit. It also shows that the stationary mean distribution of the filtered excitation determines the average phase space flux. This is true for both random and nonrandom excitations and indicates that, for the dynamical systems considered here, these two classes of excitation play substantially equivalent roles in the promotion of chaos.