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 › peer-review

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 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

Access to Document

10.1007/s11071-006-9063-7

Cite this

@article{70f47f9e4bfc4b94af184ea16bdaad30,

title = "Stability of noisy nonlinear auto-parametric systems",

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.",

keywords = "Hamiltonian, Markov processes, Martingale problem, Stochastic averaging",

author = "Namachchivaya, {N. Sri} and David Kok and Ariaratnam, {S. T.}",

note = "Funding Information: Acknowledgements N. Sri Namachchivaya would like to acknowledge the support of the National Science Foundation under grant number CMS 03-01412 and DMS 05-04581. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.",

year = "2007",

month = jan,

doi = "10.1007/s11071-006-9063-7",

language = "English (US)",

volume = "47",

pages = "143--165",

journal = "Nonlinear Dynamics",

issn = "0924-090X",

publisher = "Springer",

number = "1-3",

}

TY - JOUR

T1 - Stability of noisy nonlinear auto-parametric systems

AU - Namachchivaya, N. Sri

AU - Kok, David

AU - Ariaratnam, S. T.

N1 - Funding Information: Acknowledgements N. Sri Namachchivaya would like to acknowledge the support of the National Science Foundation under grant number CMS 03-01412 and DMS 05-04581. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

KW - Hamiltonian

KW - Markov processes

KW - Martingale problem

KW - Stochastic averaging

UR - http://www.scopus.com/inward/record.url?scp=33846074395&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846074395&partnerID=8YFLogxK

U2 - 10.1007/s11071-006-9063-7

DO - 10.1007/s11071-006-9063-7

M3 - Article

AN - SCOPUS:33846074395

VL - 47

SP - 143

EP - 165

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 1-3

ER -

Stability of noisy nonlinear auto-parametric systems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other links

Fingerprint

Cite this