Adiabatic reduction near a bifurcation in stochastically modulated systems

François Drolet and Jorge Viñals
Phys. Rev. E 57, 5036 – Published 1 May 1998
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Abstract

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 fluctuations of the fast variables above threshold are not always Gaussian and centered around the (deterministic) center manifold as was previously believed. Numerical solutions obtained for a few illustrative examples support these conclusions.

  • Received 3 December 1997

DOI:https://doi.org/10.1103/PhysRevE.57.5036

©1998 American Physical Society

Authors & Affiliations

François Drolet1 and Jorge Viñals1,2

  • 1Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4130
  • 2Department of Chemical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310-6046

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Vol. 57, Iss. 5 — May 1998

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