Stability of noisy nonlinear auto-parametric systems

N. Sri Namachchivaya; David Kok; S. T. Ariaratnam

doi:10.1007/s11071-006-9063-7

Stability of noisy nonlinear auto-parametric systems

N. Sri Namachchivaya, David Kok, S. T. Ariaratnam

Aerospace Engineering

Research output: Contribution to journal › Article

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 ε^2/3.

Original language	English (US)
Pages (from-to)	143-165
Number of pages	23
Journal	Nonlinear Dynamics
Volume	47
Issue number	1-3
DOIs	https://doi.org/10.1007/s11071-006-9063-7
State	Published - Jan 1 2007

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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

Cite this

Namachchivaya, N. S., Kok, D., & Ariaratnam, S. T. (2007). Stability of noisy nonlinear auto-parametric systems. Nonlinear Dynamics, 47(1-3), 143-165. https://doi.org/10.1007/s11071-006-9063-7

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Access to Document

10.1007/s11071-006-9063-7