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External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
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Dynamic patterns in a two-dimensional neural field with refractoriness.

Yang Qi1, Pulin Gong1

  • 1School of Physics, University of Sydney, New South Wales 2006, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
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Summary
This summary is machine-generated.

This study introduces a new two-dimensional neural-field model to understand how localized waves form and behave in neural systems. The model successfully generates various wave patterns and predicts their complex interactions and dynamics.

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Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Mathematical Biology

Background:

  • Dynamic patterns, such as localized propagating waves, are observed in various self-organizing systems, including neural systems.
  • These patterns may play significant functional roles within neural networks.

Purpose of the Study:

  • To derive and analyze a two-dimensional neural-field model incorporating refractoriness.
  • To investigate the formation mechanisms of localized waves and their dynamic behaviors.

Main Methods:

  • Development of a novel two-dimensional neural-field model with refractoriness.
  • Comparison of the new model with existing neural-field models.
  • Construction of explicit bump solutions and linear stability analysis.
  • Partial solution of the model in a comoving frame for wave analysis.

Main Results:

  • The model generates diverse localized patterns: stationary bumps, rotating waves, and longer-range propagating waves.
  • Stationary bumps transition to propagating waves under specific perturbations.
  • Propagating waves exhibit complex dynamics, including oscillatory and irregular trajectories.
  • Wave collisions demonstrate repulsive or merging behaviors influenced by collision parameters.

Conclusions:

  • The developed two-dimensional neural-field model offers a tractable framework for studying localized propagating waves.
  • The model provides insights into the formation, dynamics, and interactions of these waves in neural systems.