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Variability-sustained pattern formation in subexcitable media.

Erik Glatt1, Martin Gassel, Friedemann Kaiser

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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

Parameter variability in FitzHugh-Nagumo networks can create patterns and even trigger excitable behavior. This effect, similar to stochastic resonance, depends on coupling strength, with strong coupling inducing excitability.

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Area of Science:

  • Computational neuroscience
  • Complex systems dynamics
  • Nonlinear dynamics

Background:

  • Subexcitable media, like those modeled by FitzHugh-Nagumo elements, typically do not generate spontaneous activity.
  • Parameter heterogeneity is often considered a source of noise or complexity, rather than a driver of order.
  • Spatiotemporal stochastic resonance demonstrates that noise can enhance signal propagation in certain nonlinear systems.

Purpose of the Study:

  • To investigate the role of parameter variability (diversity) in pattern formation within a subexcitable network.
  • To explore whether parameter variability can induce a transition from subexcitable to excitable behavior.
  • To determine the influence of coupling strength on these phenomena.

Main Methods:

  • Utilized a computational network model based on FitzHugh-Nagumo elements.
  • Introduced controlled parameter variability (diversity) across the network elements.
  • Analyzed pattern formation, coherence, and transitions in network behavior as a function of variability strength and coupling strength.

Main Results:

  • Parameter variability was shown to induce pattern formation in the subexcitable network.
  • Pattern coherence peaked at intermediate levels of variability, mimicking spatiotemporal stochastic resonance.
  • A transition to excitable behavior was observed, contingent upon strong coupling between elements.
  • Weaker coupling resulted in prolonged wave lifetimes but maintained subexcitability.

Conclusions:

  • Parameter diversity can act as a constructive mechanism for pattern emergence in excitable media.
  • The transition to excitability is a robust phenomenon dependent on network connectivity.
  • This study highlights the potential for intrinsic heterogeneity to drive complex dynamics in biological and physical systems.