Dynamical bifurcation with noise
- Universidad Complutense, Madrid (Spain)
It was shown by A. Neishtadt that dynamical bifurcation, in which the control parameter is varied with a small but finite speed {epsilon}, is characterized by a delay in bifurcation, here denoted {lambda}{sub j} and depending on {epsilon}. Here we study dynamical bifurcation, in the framework and with the language of Landau theory of phase transitions, in the presence of a Gaussian noise of strength {sigma}. By numerical experiments at fixed {epsilon} = {epsilon}{sub 0}, we study the dependence of {lambda}{sub j} on {sigma} for order parameters of dimension {le}3; an exact scaling relation satisfied by the equations permits us to obtain for this the behavior for general {epsilon}. We find that in the small-noise regime {lambda}{sub j}({sigma}) {approx_equal} a{sigma}{sup (-b)}, while in the strong-noise regime {lambda}{sub j}({sigma}) {approx_equal} ce{sup (-d)}; we also measure the parameters in these formulas.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 471791
- Journal Information:
- International Journal of Theoretical Physics, Journal Name: International Journal of Theoretical Physics Journal Issue: 4 Vol. 34; ISSN IJTPBM; ISSN 0020-7748
- Country of Publication:
- United States
- Language:
- English
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