Journal
NONLINEAR DYNAMICS
Volume 36, Issue 2-4, Pages 437-453Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/B:NODY.0000045516.65717.21
Keywords
bounded noise; moment Lyapunov exponents; parametric resonance
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The dynamic stability of a two-dimensional system under bounded noise excitation with a narrow band characteristic is studied through the determination of the pth moment Lyapunov exponent and the Lyapunov exponent. The case when the system is in primary parametric resonance in the absence of noise is considered and the effect of noise on the parametric resonance is investigated. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For small amplitudes of the bounded noise, a method of singular perturbation is applied to determine analytical expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in excellent agreement with those obtained using numerical approaches.
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