International Journal of Theoretical Physics

, Volume 34, Issue 4, pp 595–603 | Cite as

Dynamical bifurcation with noise

  • Giuseppe Gaeta


It was shown by A. Neishtadt that dynamical bifurcation, in which the control parameter is varied with a small but finite speed ∈, is characterized by adelay in bifurcation, here denoted λj and depending on ∈. 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 σ. By numerical experiments at fixed ∈ = ∈0, we study the dependence of λj on a for order parameters of dimension ≤3; an exact scaling relation satisfied by the equations permits us to obtain for this the behavior for general ∈. We find that in the smallnoise regime λj(σ) ≃aσ(b), while in the strong-noise regime λj(σ) − ce(−d); we also measure the parameters in these formulas.


Phase Transition Field Theory Elementary Particle Quantum Field Theory Numerical Experiment 
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Giuseppe Gaeta
    • 1
  1. 1.Departamento de Fisica Teorica II, Metodos Matematicos de la FisicaUniversidad ComplutenseMadridSpain

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