Stability of synchronous states in sparse neuronal networks

Afifurrahman, Ekkehard Ullner, Antonio Politi

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The stability of synchronous states is ana- lyzed in the context of two populations of inhibitory and excitatory neurons, characterized by two different pulse-widths. The problem is reduced to that of deter- mining the eigenvalues of a suitable class of sparse ran- dom matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude perturbations, is per- formed 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
Pages (from-to)733-743
Number of pages11
JournalNonlinear Dynamics
Early online date24 Aug 2020
Publication statusPublished - 24 Aug 2020

Bibliographical note

Acknowledgements: Afifurrahman was supported by the Ministry of Finance of the Republic of Indonesia through the Indonesia Endowment Fund for Education (LPDP) (grant number: PRJ2823/LPDP/2015)
Compliance with ethical standards
Conflict of interest The authors declare that they have no con-
flict of interest.


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


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