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Spatiotemporal patterns driven by autocatalytic internal reaction noise.

David Hochberg1, M-P Zorzano, Federico Morán

  • 1Centro de Astrobiología [Consejo Superior de Investigaciones Científicas- Instituto Nacional de Técnica Aeroespacial (CSIC-INTA)] Carretera Ajalvir Km. 4, 28850 Torrejón de Ardoz, Madrid, Spain. hochberg@laeff.esa.es

The Journal of Chemical Physics
|June 25, 2005
PubMed
Summary

Strong internal reaction noise significantly alters spatial patterns in reaction-diffusion models like the Gray-Scott model. Novel patterns emerge due to noise, even in parameter regions typically showing homogeneous solutions.

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Area of Science:

  • Chemical kinetics
  • Non-linear dynamics
  • Computational modeling

Background:

  • Reaction-diffusion models are crucial for understanding pattern formation.
  • Intrinsic fluctuations can significantly impact model dynamics.
  • The Gray-Scott model is a well-established system for studying pattern formation.

Purpose of the Study:

  • To investigate the influence of intrinsic local-density fluctuations on reaction-diffusion models.
  • To explore spatial patterns arising from strong internal reaction noise.
  • To analyze the impact of noise on the Gray-Scott model.

Main Methods:

  • Numerical simulations of the Gray-Scott model with a constant external source.
  • Formulation of a continuum field theory from the master equation.

Related Experiment Videos

  • Derivation and application of Langevin descriptions (stochastic differential equations).

    • Main Results:

    • Strong internal multiplicative noise, comparable to reaction rates, was characterized.
    • Many complex patterns observed in the absence of noise were disrupted.
    • Novel spatial patterns were induced by reaction noise in previously homogeneous regions.

    Conclusions:

    • Intrinsic fluctuations play a critical role in determining spatial patterns in reaction-diffusion systems.
    • Reaction noise can generate complex spatial structures not predicted by mean-field theories.
    • The findings highlight the importance of considering noise in modeling chemical and biological pattern formation.