TY - JOUR
T1 - The asymptotic stability of a noisy non-linear oscillator
AU - Arnold, L.
AU - Imkeller, P.
AU - Sri Namachchivaya, N.
N1 - Funding Information:
We would like to thank Peter Baxendale for helpful and simulating discussions during the preparation of this paper. Sri Namachchivaya would also like to acknowledge the support of the Office of Naval Research under grant number N000140110647, and National Science Foundation under grant numbers CMS 00-84944 and CMS 03-01412.
PY - 2004/1/22
Y1 - 2004/1/22
N2 - The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers oscillator driven by either a multiplicative or an additive white-noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity √ε and dissipation ε the exponent grows in proportion with ε1/3.
AB - The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers oscillator driven by either a multiplicative or an additive white-noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity √ε and dissipation ε the exponent grows in proportion with ε1/3.
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U2 - 10.1016/S0022-460X(03)00211-6
DO - 10.1016/S0022-460X(03)00211-6
M3 - Article
AN - SCOPUS:0345870000
SN - 0022-460X
VL - 269
SP - 1003
EP - 1029
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 3-5
ER -