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Published on: August 15, 2020

Additive global noise delays Turing bifurcations.

Axel Hutt1, Andre Longtin, Lutz Schimansky-Geier

  • 1Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N-6N5, Canada. ahutt@uottawa.ca

Physical Review Letters
|August 7, 2007
PubMed
Summary

We used a stochastic center manifold method to study noise-induced phase transitions in the Swift-Hohenberg equation. Our findings reveal a novel postponement of the Turing bifurcation due to additive noise.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Computational physics

Background:

  • The Swift-Hohenberg equation models pattern formation in various physical systems.
  • Understanding noise-induced transitions is crucial for predicting system behavior.
  • Previous methods struggled to accurately capture higher-order noise effects.

Purpose of the Study:

  • To investigate noise-induced phase transitions in the stochastic Swift-Hohenberg equation.
  • To analyze the impact of additive noise on bifurcations.
  • To develop a robust theoretical framework for nonlinear spatial systems.

Main Methods:

  • Application of the stochastic center manifold method.
  • Analysis of reduced mode equations derived from Fourier decomposition.
  • Comparison of theoretical predictions with numerical simulations.

Main Results:

  • The stochastic center manifold method accurately predicts pitchfork bifurcations.
  • A novel postponement of the Turing bifurcation was observed at higher perturbation orders due to additive noise.
  • Excellent agreement between theoretical results and numerical simulations for both reduced and full systems.

Conclusions:

  • The stochastic center manifold method is effective for analyzing noise-induced phase transitions.
  • Additive noise can significantly alter bifurcation dynamics in nonlinear systems.
  • The findings are generalizable to a wide range of nonlinear spatial systems.