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Neuronal dynamics under periodic stimuli.

K Gopalsamy1, S Mohamad

  • 1School of Informatics and Engineering, Flinders University of South Australia, Bedford Park SA 5042, Australia. gopal@infoeng.flinders.edu.au

International Journal of Neural Systems
|May 30, 2002
PubMed
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This study examines a single dissipative Hopfield-type neuron

Area of Science:

  • Computational neuroscience
  • Artificial neural networks
  • Dynamical systems

Background:

  • Hopfield-type neural networks are models of associative memory.
  • Dissipative neurons and self-interaction introduce unique dynamics.
  • Periodic external stimuli can drive complex neuronal behavior.

Purpose of the Study:

  • To analyze the convergence properties of a single dissipative Hopfield-type neuron with self-interaction.
  • To establish conditions for associative encoding and recall of periodic patterns.
  • To investigate both continuous-time and discrete-time models.

Main Methods:

  • Mathematical analysis of neuronal dynamics.
  • Derivation of sufficient conditions for pattern recall.
  • Investigation of global asymptotic stability.

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Main Results:

  • Sufficient conditions for associative encoding and recall were established.
  • Both continuous-time-continuous-state and discrete-time-continuous-state models were analyzed.
  • Associative recall is guaranteed when neuronal gain is dominated by dissipation.

Conclusions:

  • The global asymptotic stability of the encoded pattern ensures reliable associative recall.
  • The findings provide insights into the memory capabilities of dissipative neural models.
  • This work contributes to understanding neural information processing under periodic stimulation.