Maximal Lyapunov exponent and almost-sure sample stability for second-order linear stochastic system

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

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

The principal resonance of second-order system to random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The explicit asymptotic formulas for the maximum Lyapunov exponent is obtained. The almost-sure stability or instability of the stochastic Mathieu system depends on the sign of the maximum Lyapunov exponent.

Original languageEnglish
Pages (from-to)609-614
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume38
Issue number4
DOIs
StatePublished - Jun 2003

Keywords

  • Almost-sure sample stability
  • Maximal Lyapunov exponent
  • Multiple scale method

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