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Resonantly forced inhomogeneous reaction-diffusion systems.

C. J. Hemming1, R. Kapral

  • 1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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We investigated spatiotemporal patterns in reaction-diffusion systems with random forcing. Periodic forcing with random amplitude creates novel structures like compound fronts and pulses, affecting spiral wave dynamics.

Area of Science:

  • Physics
  • Chemical Engineering
  • Applied Mathematics

Background:

  • Oscillatory reaction-diffusion systems exhibit complex spatiotemporal patterns.
  • Periodic forcing and quenched disorder significantly influence pattern dynamics.

Purpose of the Study:

  • To investigate the dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems under periodic forcing with spatially random amplitude.
  • To characterize front roughening, pattern nucleation, and the formation of novel structures like compound fronts and pulses.

Main Methods:

  • Utilized the resonantly forced complex Ginzburg-Landau equation for quenched disorder studies.
  • Employed the 3:1 forced FitzHugh-Nagumo system to analyze time-dependent, spatially varying forcing fields.
  • Characterized pattern formation and front dynamics through numerical simulations.

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Main Results:

  • Observed front roughening and spontaneous nucleation of target patterns in the presence of quenched disorder.
  • Demonstrated that periodic variation of random forcing amplitude breaks symmetry, leading to inequivalent front velocities.
  • Identified the formation of "compound fronts" and "pulses" due to unequal front velocities.
  • Studied spiral wave dynamics in systems exhibiting compound fronts.

Conclusions:

  • Periodic forcing with spatially random amplitude introduces significant asymmetry, leading to emergent complex structures.
  • Compound fronts and pulses represent novel phenomena arising from the interplay of forcing and system dynamics.
  • The study provides insights into pattern formation and stability in driven complex systems.