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Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Statistical Physics

Background:

  • Ongoing neural activity in brain networks exhibits intrinsic stochasticity, with firing rate fluctuations persisting even in isolated networks.
  • This seemingly random behavior arises from deterministic chaos due to synaptic coupling disorder, yet an effective theory for finite neuron assemblies is missing.

Purpose of the Study:

  • To develop an effective theory for the network dynamics of finite spiking neuron assemblies.
  • To analytically characterize the finite-size noise influencing neural network dynamics.

Main Methods:

  • Extended the population density approach by incorporating an activity- and size-dependent stochastic source.
  • Formulated a Fokker-Planck equation for membrane potential density to describe network dynamics.
  • Analytically characterized the embedded finite-size noise.

Main Results:

  • Developed a self-consistent, nonperturbative description of the instantaneous firing rate (ν(t)) for spiking neuron networks.
  • Achieved excellent agreement between the theory's predictions and detailed simulation results.
  • Observed size-dependent smearing of critical dynamics during synchronization phase transitions.

Conclusions:

  • The developed theory provides a robust framework for understanding stochastic dynamics in finite spiking neuron networks.
  • The model successfully captures network behavior across different regimes, including synchronization.
  • Finite-size noise plays a crucial role in shaping neural network dynamics.