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Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
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Published on: June 29, 2018

Collective oscillations in disordered neural networks.

Simona Olmi1, Roberto Livi, Antonio Politi

  • 1Physics Department, via Sansone, 1-I-50019 Sesto Fiorentino, Italy. simona.olmi@fi.isc.cnr.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary

Disorder in neural networks causes weak chaos, similar to the Kuramoto model. This chaos diminishes as network size increases, simplifying dynamics in large systems.

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Area of Science:

  • Computational neuroscience
  • Complex systems dynamics
  • Nonlinear dynamics

Background:

  • Leaky integrate-and-fire neurons are fundamental models in computational neuroscience.
  • Collective oscillations and synchronization are key phenomena in neural networks.
  • Disorder, both quenched and annealed, significantly impacts network dynamics.

Purpose of the Study:

  • To investigate the onset of collective oscillations in excitatory pulse-coupled networks of leaky integrate-and-fire neurons.
  • To analyze the effects of quenched and annealed disorder on network dynamics and chaos.
  • To compare the behavior of these neural networks to the Kuramoto model.

Main Methods:

  • Simulations of pulse-coupled leaky integrate-and-fire neural networks.
  • Analysis of Lyapunov exponents to quantify chaos.
  • Mathematical analysis of network dynamics in the thermodynamic limit.
  • Comparison with the Kuramoto model for coupled oscillators.

Main Results:

  • Disorder induces a weak form of chaos, analogous to the Kuramoto model.
  • The maximum Lyapunov exponent scales to zero as N approaches infinity, with distinct scaling for different disorder types.
  • In the thermodynamic limit, network dynamics simplify to a homogeneous system with scaled coupling.
  • The Lyapunov spectrum of the collective state scales as 1/N^2.

Conclusions:

  • Disorder in neural networks leads to a finite-size effect on chaos, which vanishes in the thermodynamic limit.
  • The dynamics of disordered neural networks can be effectively reduced to simpler models in large-N limits.
  • The findings provide insights into the robustness and collective behavior of neural systems under varying conditions.