Adiabatic reduction near a bifurcation in stochastically modulated systems

@article{Drolet1997AdiabaticRN,
  title={Adiabatic reduction near a bifurcation in stochastically modulated systems},
  author={François Perron Drolet and Jorge Vi{\~n}als},
  journal={Physical Review E},
  year={1997},
  volume={57},
  pages={5036-5043}
}
We reexamine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation are obtained near threshold for the pitchfork and transcritical bifurcations. Correlations between fast variables and random modulation may shift the effective bifurcation point by an amount proportional to the intensity of the fluctuations. We also find that… 

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