Stochastically Perturbed Bifurcations
The methods of normal form and stochastic averaging are used appropriately to study nonlinear stochastic dynamical systems. General results obtained by those procedures are applied to study the effect of stochastic excitations on nonlinear systems which exhibit co-dimension one bifurcations. As an application the stochastic version of the Lorenz model is considered.
Unable to display preview. Download preview PDF.
- 1.Carr, J.: Applications of Center Manifold Theory, Appl. Math. Sci., Vol. 35, Springer-Verlag, New York, 1981.Google Scholar
- 2.Golubitsky, M. and Schaeffer, D. G.: Singularities and Groups in Bifurcation Theory, Appl. Math. Sci., Vol. 51, Springer-Verlag, New York, 1985.Google Scholar
- 3.Guckenheimer, J. and Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Vol. 42, Springer-Verlag, New York, 1983.Google Scholar
- 6.Sri Namachchivaya, N.: Hopf bifurcation in the presence of both parametric and external stochastic excitations, J. Appl. Mech. (ASME), (to appear).Google Scholar
- 7.Sri Namachchivaya, N. and Lin, Y. K.: Application of stochastic averaging for nonlinear dynamical systems with high damping, J. Prob. Engr. Mech. (to appear).Google Scholar
- 8.Sri Namachchivaya, N.: Bifurcations in nonconservative systems in the presence of noise, in preparation.Google Scholar
- 9.Sethna, P. R.: On normal forms, averaging and symbolic manipulators, SIAM J. Appl. Math. (to appear).Google Scholar