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Related Experiment Videos

Spatiotemporal structures in a model with delay and diffusion.

M Bestehorn1, E V Grigorieva, S A Kaschenko

  • 1Department of Theoretical Physics II, Brandenburg University of Technology, 03013 Cottbus, Germany. bes@physik.tu-cottbus.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2004
PubMed
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Even minimal diffusion can create space-time turbulence in pattern-forming systems at the instability threshold. Further analysis reveals synchronized spiral and target states emerge at higher thresholds.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Complex systems

Background:

  • Investigating pattern formation governed by differential-difference equations with diffusion.
  • Understanding the transition from stable states to complex dynamic behaviors.

Purpose of the Study:

  • To demonstrate how diffusion influences pattern formation.
  • To analyze the emergence of turbulence and synchronized states.

Main Methods:

  • Normal form analysis to derive a complex Ginzburg-Landau equation.
  • Asymptotic methods to represent the system as a cellular automaton network.

Main Results:

  • An arbitrarily small diffusion coefficient induces space-time turbulence at the instability threshold.

Related Experiment Videos

  • Turbulent structures transition to synchronized spiral and target states well above the threshold.

    • Conclusions:

    • Diffusion plays a critical role in pattern formation, triggering turbulence even at low levels.
    • The system exhibits a transition from turbulence to ordered synchronized states, explainable by cellular automaton dynamics.