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.
Bibliographical noteAcknowledgements: 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)
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- Stability analysis
- Neuronal Network
- Sparse Network
- Neuronal network
- Sparse network