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Patterning via Optical Saturable Transitions - Fabrication and Characterization
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Published on: December 11, 2014

Fluctuation-driven Turing patterns.

Thomas Butler1, Nigel Goldenfeld

  • 1Department of Physics and Institute for Genomic Biology, University of Illinois at Urbana Champaign, 1110 West Green Street, Urbana, IL 61801, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

Introducing intrinsic noise into Turing models for pattern formation generates "quasipatterns." These quasipatterns form without fine-tuning parameters, offering a more realistic approach to ecological modeling.

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Area of Science:

  • Theoretical ecology
  • Mathematical biology
  • Chemical kinetics

Background:

  • Turing mechanism models are widely used for diffusion-driven pattern formation.
  • Existing models often require fine-tuning parameters or unrealistic diffusivity scales.
  • This limits their applicability to real-world systems.

Purpose of the Study:

  • To investigate the effect of intrinsic noise on Turing models for pattern formation.
  • To determine if noise can alleviate the need for fine-tuning parameters.
  • To explore the formation of novel patterns in ecological models.

Main Methods:

  • Developed a generic model of ecological pattern formation incorporating intrinsic noise.
  • Analyzed the parameter space for pattern formation under noisy conditions.
  • Characterized the emergent patterns and compared them to standard Turing patterns.

Main Results:

  • Inclusion of intrinsic noise leads to the formation of "quasipatterns".
  • Quasipatterns emerge in generic regions of the parameter space.
  • These patterns are experimentally distinguishable from standard Turing patterns.

Conclusions:

  • Intrinsic noise in Turing models removes the need for unphysical fine-tuning of parameters.
  • Quasipatterns offer a more robust and realistic mechanism for pattern formation in ecological systems.
  • This approach enhances the applicability of Turing models to real-world phenomena.