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Related Experiment Video

Updated: May 24, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

Published on: June 24, 2015

Neural fields with fast learning dynamic kernel.

A H Abbassian1, M Fotouhi, M Heidari

  • 1School of Mathematics, Institute for Research in Fundamental Sciences-IPM, P.O. Box 19395-5746, Tehran, Iran. abbnet@mail.ipm.ir

Biological Cybernetics
|March 9, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a modified firing-rate model with Hebbian synaptic plasticity, demonstrating stable rest states, bumps, and traveling waves. The research explores various synaptic connection types, offering insights into neural network dynamics.

Related Experiment Videos

Last Updated: May 24, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

Published on: June 24, 2015

Area of Science:

  • Computational Neuroscience
  • Mathematical Biology
  • Systems Neuroscience

Background:

  • Neural network dynamics are often modeled using firing-rate models.
  • Synaptic plasticity, particularly Hebbian-type learning, plays a crucial role in shaping network activity.
  • Understanding the stability and existence of different network states is fundamental.

Purpose of the Study:

  • To introduce and analyze a modified firing-rate model incorporating Hebbian-type synaptic plasticity.
  • To investigate the existence and stability of various network solutions, including rest states, bumps, and traveling waves.
  • To examine the influence of different synaptic kernel types (exponential, Mexican hat, periodic) on model dynamics.

Main Methods:

  • Development of a modified firing-rate model with Hebbian synaptic plasticity.
  • Analytical methods to prove the existence and stability of rest state solutions.
  • Use of Evans function to analyze the stability of bump solutions for specific synaptic kernels.
  • Numerical simulations and analysis to illustrate and verify solutions.

Main Results:

  • Existence and stability conditions for rest state solutions were proven for exponential and Mexican hat kernels.
  • Bump solutions were demonstrated for two synaptic kernel types, with stability analyzed via Evans function for specific kernel coefficient strengths (KCS).
  • Traveling wave solutions were shown to exist for exponential synaptic connections.

Conclusions:

  • The modified firing-rate model with Hebbian plasticity supports diverse network states.
  • Synaptic kernel type and its strength significantly influence the stability and existence of these states.
  • The study provides a theoretical and numerical framework for understanding neural dynamics with adaptive synapses.