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Delay-sustained pattern formation in subexcitable media.

Martin Gassel1, Erik Glatt, Friedemann Kaiser

  • 1Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 4a, 64289 Darmstadt, Germany. martin.gassel@physik.tu-darmstadt.de

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Summary

Time-delayed feedback can induce excitable behavior in neuronal networks. This feedback enhances pattern formation and coherence, even when applied to only half the network elements.

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Area of Science:

  • Computational neuroscience
  • Complex systems

Background:

  • Subexcitable media, like neuronal networks, typically exhibit limited wave propagation without external influence.
  • Neuronal dynamics are often modeled using systems like the FitzHugh-Nagumo model.

Purpose of the Study:

  • To investigate the effect of time-delayed feedback on pattern formation in subexcitable neuronal networks.
  • To determine the conditions under which feedback can induce excitable behavior and enhance pattern coherence.

Main Methods:

  • Utilizing a network of FitzHugh-Nagumo elements to model neuronal dynamics.
  • Applying time-delayed feedback with varying parameters and spatial correlation.
  • Analyzing pattern formation, wave propagation, and noise-induced pattern coherence.

Main Results:

  • Time-delayed feedback can sustain pattern formation and induce excitable behavior in subexcitable media.
  • Feedback significantly enhances the coherence of noise-induced patterns, with a resonance-like dependence on delay time.
  • Controlling approximately half of the network elements is sufficient to achieve excitable behavior.
  • Spatially correlated feedback distributions influence pattern formation.

Conclusions:

  • Time-delayed feedback is a viable mechanism for controlling and enhancing dynamics in neuronal networks.
  • The findings suggest potential applications in modulating neural tissue activity.
  • Network element control and feedback correlation are critical factors for pattern formation.