Stability of synchronous states in sparse neuronal networks

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Abstract

The stability of synchronous states is analyzed in the context of two populations of inhibitory and excitatory neurons, characterized by two different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable class of sparse random matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude perturbations, is performed in the limit of narrow pulses, finding that the overall stability depends crucially on the relative pulse-width. This has implications for the overall property of the asynchronous (balanced) regime.

Original languageEnglish
Number of pages11
JournalNonlinear Dynamics
Early online date24 Aug 2020
DOIs
Publication statusE-pub ahead of print - 24 Aug 2020

Keywords

  • Stability analysis
  • Synchronization
  • Neuronal Network
  • Sparse Network
  • Neuronal network
  • Sparse network

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