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Dynamics of Turing patterns under spatiotemporal forcing.

S Rüdiger1, D G Míguez, A P Muñuzuri

  • 1Departament E.C.M., Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain.

Physical Review Letters
|April 12, 2003
PubMed
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We explored how Turing patterns respond to traveling wave forcing, discovering new dynamics like modulated waves and soliton solutions. These findings were confirmed experimentally in a chemical reaction.

Area of Science:

  • Chemical Kinetics
  • Nonlinear Dynamics
  • Pattern Formation

Background:

  • Turing patterns are fundamental to understanding pattern formation in reaction-diffusion systems.
  • Spatiotemporal forcing can significantly alter the dynamics of these patterns.

Purpose of the Study:

  • To investigate the dynamical response of Turing patterns to traveling-wave forcing.
  • To identify and characterize novel dynamical behaviors and solutions induced by this forcing.

Main Methods:

  • Theoretical analysis of pattern dynamics under spatiotemporal forcing.
  • Numerical determination of stability diagrams for propagating modes in the Lengyel-Epstein model.
  • Experimental validation using light modulation in a photosensitive Belousov-Zhabotinsky type reaction (chlorine dioxide-iodine-malonic acid).

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Main Results:

  • Spatial resonance can induce temporally modulated traveling waves.
  • Localized traveling solitonlike solutions, generalizing previous work, were observed.
  • The stability diagram for propagating modes in the Lengyel-Epstein model was numerically mapped.

Conclusions:

  • Spatiotemporal forcing offers a route to new, generic dynamical behaviors in Turing patterns.
  • The observed solitonlike solutions represent a significant extension of known soliton dynamics.
  • Experimental results validate the theoretical predictions, demonstrating control over pattern dynamics.