Stochastic Stability of Two Coupled Oscillators in Resonance

N Sri Namachchivaya,N Ramakrishnan,L Vedula,H J Van Roessel

doi:10.1007/978-94-010-0179-3_14

Stochastic Stability of Two Coupled Oscillators in Resonance

N Sri Namachchivaya, N Ramakrishnan + Show 2 more

https://doi.org/10.1007/978-94-010-0179-3_14

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Publication Date: Jan 1, 2003

Citations: 8

Affiliation: University of Illinois Urbana-Champaign, University of Alberta

#Coupled Oscillators #Girsanov Transformation + Show 8 more

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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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