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Updated: May 16, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Stability of the splay state in networks of pulse-coupled neurons
Simona Olmi1, Antonio Politi, Alessandro Torcini
1Istituto dei Sistemi Complessi, CNR - Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019, Sesto Fiorentino, Italy. alessandro.torcini@cnr.it.
Abstract:
We analytically investigate the stability of splay states in the networks of N globally pulse-coupled phase-like models of neurons. We develop a perturbative technique which allows determining the Floquet exponents for a generic velocity field and implement the method for a given pulse shape. We find that in the case of discontinuous velocity fields, the Floquet spectrum scales as 1/N2 and the stability is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape, but it is independent of the velocity field.PACS: 05.45.Xt, 84.35.+i, 87.19.lj.
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