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Regular patterns in dichotomically driven activator-inhibitor dynamics.

X Sailer1, D Hennig, V Beato

  • 1Institut für Physik, Humboldt-Universität zu Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 29, 2006
PubMed
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Dichotomous fluctuations can induce Turing patterns in excitable systems. Different switching rates reveal distinct mechanisms, including boundary instability, effective bistability, and a novel spatial structure formation, leading to pattern emergence.

Area of Science:

  • * Theoretical physics
  • * Nonlinear dynamics
  • * Computational neuroscience

Background:

  • * Turing pattern formation is crucial for understanding biological morphogenesis.
  • * Excitable systems, like the FitzHugh-Nagumo model, exhibit complex dynamics.
  • * Fluctuations can significantly alter system behavior, but their role in pattern formation is complex.

Purpose of the Study:

  • * To investigate Turing pattern formation in an extended FitzHugh-Nagumo system with dichotomous fluctuations.
  • * To analyze the influence of fluctuation switching rates and spatial/temporal variations.
  • * To elucidate the distinct mechanisms by which fluctuations induce pattern formation.

Main Methods:

  • * Simulation of an extended FitzHugh-Nagumo system with additive dichotomous noise.

Related Experiment Videos

  • * Analysis of spatial and temporal fluctuation characteristics.
  • * Application of a nonlinear map approach to study system stability and bifurcations.

    • Main Results:

    • * Dichotomous fluctuations can destabilize the homogeneous steady state, inducing Turing patterns.
    • * Three distinct mechanisms of pattern formation were identified based on switching rates: boundary instability (slow), effective bistability (high), and a novel twofold fluctuation influence (medium).
    • * Static dichotomous disorder also leads to Turing patterns for finite correlation lengths.

    Conclusions:

    • * Additive dichotomous fluctuations are a viable mechanism for generating Turing patterns in excitable systems.
    • * The switching rate of fluctuations critically determines the pattern formation mechanism.
    • * The study reveals novel pathways for pattern emergence driven by noise in biological and physical systems.