Abstract
We obtain an approximation for the moment Lyapunov exponent of two coupled oscillators with commensurable frequencies driven by a small intensity real noise. A stochastic averaging scheme along with a Girsanov transformation and the Feynman-Kac formula are used to explicitly obtain the eigenvalue problem for the moment Lyapunov exponent. An orthogonal expansion for the eigenvalue problem based on Galerkin method is used to derive the stability results.
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Namachchivaya, N.S., Ramakrishnan, N., Van Roessel, H.J., Vedula, L. (2003). Stochastic Stability of Two Coupled Oscillators in Resonance. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_14
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DOI: https://doi.org/10.1007/978-94-010-0179-3_14
Publisher Name: Springer, Dordrecht
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