Application of Stochastic Averaging for Nonlinear Dynamical Systems with High Damping

  • N. Sri Namachchivaya
  • Y. K. Lin
Part of the Lecture Notes in Engineering book series (LNENG, volume 31)


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.


Hopf Bifurcation Bifurcation Point Center Manifold Stochastic Average Double Pendulum 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • N. Sri Namachchivaya
    • 1
  • Y. K. Lin
    • 2
  1. 1.Department of Aeronautical and Astronautical EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Center for Applied Stochastics ResearchFlorida Atlantic UniversityBoca RatonUSA

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