Invariant measures and Lyapunov exponents for stochastic Mathieu system

Haiwu Rong; Guang Meng; Xiangdong Wang; Wei Xu; Tong Fang

doi:10.1023/A:1021208631414

Invariant measures and Lyapunov exponents for stochastic Mathieu system

Haiwu Rong, Guang Meng, Xiangdong Wang, Wei Xu, Tong Fang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

The principal resonance of the stochastic Mathieu oscillator to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent are obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.

Original language	English
Pages (from-to)	313-321
Number of pages	9
Journal	Nonlinear Dynamics
Volume	30
Issue number	4
DOIs	https://doi.org/10.1023/A:1021208631414
State	Published - Dec 2002

Keywords

Almost-sure sample stability
Maximum Lyapunov exponent
Multiple scale method
Principal resonance
Stochastic Mathieu system

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abstract = "The principal resonance of the stochastic Mathieu oscillator to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent are obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.",

keywords = "Almost-sure sample stability, Maximum Lyapunov exponent, Multiple scale method, Principal resonance, Stochastic Mathieu system",

author = "Haiwu Rong and Guang Meng and Xiangdong Wang and Wei Xu and Tong Fang",

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T1 - Invariant measures and Lyapunov exponents for stochastic Mathieu system

AU - Rong, Haiwu

AU - Meng, Guang

AU - Wang, Xiangdong

AU - Xu, Wei

AU - Fang, Tong

PY - 2002/12

Y1 - 2002/12

N2 - The principal resonance of the stochastic Mathieu oscillator to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent are obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.

AB - The principal resonance of the stochastic Mathieu oscillator to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent are obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.

KW - Almost-sure sample stability

KW - Maximum Lyapunov exponent

KW - Multiple scale method

KW - Principal resonance

KW - Stochastic Mathieu system

UR - http://www.scopus.com/inward/record.url?scp=0036926475&partnerID=8YFLogxK

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DO - 10.1023/A:1021208631414

M3 - 文章

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SN - 0924-090X

VL - 30

SP - 313

EP - 321

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 4

ER -

Invariant measures and Lyapunov exponents for stochastic Mathieu system

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Keywords

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