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Noisy-flow-induced instability in a reaction-diffusion system.

Shibashis Paul1, Shyamolina Ghosh1, Deb Shankar Ray1

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India.

Physical Review. E
|January 14, 2017
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Summary
This summary is machine-generated.

We found that fluctuating flow velocities in reaction-diffusion-advection systems can break symmetry, leading to traveling waves. This instability arises from dichotomous noise in the advection term.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Mathematical Biology

Background:

  • Reaction-diffusion-advection systems model various spatio-temporal phenomena.
  • Flow velocity fluctuations can significantly alter system dynamics.
  • Understanding noise-induced transitions is crucial in complex systems.

Purpose of the Study:

  • To investigate the impact of dichotomous noise in advection on reaction-diffusion systems.
  • To derive conditions for instability induced by noisy flow.
  • To demonstrate symmetry breaking and pattern formation in a specific model.

Main Methods:

  • Analysis of a generic reaction-diffusion-advection system with dichotomous noise.
  • Derivation of a general instability condition in the flow velocity-correlation rate plane.
  • Numerical simulations using the Gierer-Meinhardt model with activator-inhibitor kinetics.

Main Results:

  • A general condition for noisy-flow-induced instability was established.
  • Dichotomous noise in differential flow was shown to induce symmetry breaking.
  • Stable homogeneous states transitioned to traveling waves due to noise.

Conclusions:

  • Noisy advection can destabilize homogeneous states in reaction-diffusion systems.
  • Symmetry breaking and pattern formation (traveling waves) are key outcomes.
  • The findings provide insights into noise-driven pattern formation in biological and chemical systems.