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Drifting pattern domains in a reaction-diffusion system with nonlocal coupling.

Ernesto M Nicola1, Michal Or-Guil, Wilfried Wolf

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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Drifting pattern domains (DPDs) emerge from simulations of reaction-diffusion models. These moving wave patches are caused by locked interface velocities, driven by the lack of space-time defects near the boundaries.

Area of Science:

  • Reaction-diffusion systems
  • Nonlocal coupling dynamics
  • Pattern formation in nonlinear systems

Background:

  • Reaction-diffusion models exhibit complex spatiotemporal patterns.
  • Turing patterns represent stationary states, while traveling waves represent propagating structures.
  • Bistability between these patterns arises from specific bifurcation points.

Purpose of the Study:

  • Investigate the emergence and dynamics of drifting pattern domains (DPDs).
  • Analyze the behavior of interfaces between stationary (Turing) patterns and traveling waves.
  • Understand the underlying mechanisms causing DPDs in nonlocal reaction-diffusion models.

Main Methods:

  • Simulations of a reaction-diffusion model with nonlocal coupling.
  • Analysis of a codimension-2 Turing-wave bifurcation (TWB).

Related Experiment Videos

  • Investigation of single interface dynamics between Turing and wave patterns.

    • Main Results:

    • Observed drifting pattern domains (DPDs) in simulations.
    • DPDs occur in a region of bistability between Turing patterns and traveling waves.
    • DPDs result from locked interface velocities due to the absence of space-time defects.

    Conclusions:

    • The absence of space-time defects near interfaces is crucial for DPD formation.
    • Interface velocity locking mechanism explains the existence of DPDs.
    • DPDs represent a distinct dynamic state in nonlocal reaction-diffusion systems.