Application of Stochastic Averaging for Nonlinear Dynamical Systems with High Damping
The asymptotic behavior of coupled nonlinear dynamical systems in the presence of noise is studied using the method of stochastic averaging. It is shown that, for systems with rapidly oscillating and decaying components, the stochastic averaging technique yields a set of equations of considerably smaller dimension, and the resulting equations are simpler. General results of this method are applied to stochastically perturbed nonlinear nonconservative systems in R4. It is shown that in such systems the contribution of the stochastic components in the damped modes to the drift term of the critical mode may be beneficial in terms of stability in certain cases.
KeywordsHopf Bifurcation Bifurcation Point Center Manifold Stochastic Average Double Pendulum
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- 1.Stratonovich, R. L. Topics in the Theory of Random Noise, Vol. 1, Gordon and Breach, New York, 1963.Google Scholar
- 9.Sri Namachchivaya, N. Hopf bifurcation in the presence of both parametric and external stochastic excitation, to appear, Journal of Applied Mechanics (ASME).Google Scholar
- 11.Sri Namachchivaya, N. Bifurcations in nonconservative systems in the presence of noise, in preparation.Google Scholar