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Microscopic instability in recurrent neural networks.

Yuzuru Yamanaka1, Shun-ichi Amari2, Shigeru Shinomoto1

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Even with stable overall brain activity, individual neurons can be unstable. This study shows diverse microscopic dynamics within stable neuronal networks, suggesting complex fluctuations in real brain networks.

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Statistical Physics

Background:

  • Stable macroscopic brain activity can arise from complex underlying neuronal dynamics.
  • Understanding the relationship between microscopic neuronal behavior and macroscopic network states is crucial for neuroscience.

Purpose of the Study:

  • To investigate the microscopic stability of neuronal networks exhibiting stable macroscopic dynamics (monostable, bistable, or periodic).
  • To explore the variety of dynamical states possible at the microscopic level within these stable macroscopic states.

Main Methods:

  • Analysis of a random network of neurons.
  • Examination of neuronal dynamics under conditions of stable macroscopic activity.
  • Characterization of microscopic instability within defined macroscopic states.

Main Results:

  • Neuronal networks with stable macroscopic dynamics can exhibit a wide range of microscopic dynamical states.
  • Microscopic instability is compatible with macroscopic stability across different network states.
  • The observed variety of states in a simple network suggests even greater complexity in real neural systems.

Conclusions:

  • Macroscopic stability in neuronal networks does not preclude diverse microscopic instabilities.
  • Simple random networks can display rich dynamics, hinting at the complexity of biological neural networks.
  • Findings imply that real neural networks likely possess abundant microscopic fluctuations due to their complex structure.