2008/01/01 by Simona Olmi, Antonio Politi, Alessandro Torcini +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Health Professions · Mathematics · Medicine · Neuroscience · Physics and Astronomy · Social Sciences · #Adolescent Sexual and Reproductive Health #Computer science #Discontinuity (linguistics) #Economic growth #Economics #Family medicine #Field (mathematics) #Floquet theory #HIV/AIDS Research and Interventions #Human immunodeficiency virus (HIV) #Immunology #Jump #Law #Malaria #Mathematical analysis #Mathematics #Medicine #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Phase (matter) #Physics #Political action #Political science #Politics #Poverty, Education, and Child Welfare #Psychiatry #Public administration #Public relations #Pulse (music) #Pure mathematics #Quantum mechanics #Sign (mathematics) #Spectrum (functional analysis) #Stability (learning theory) #State (computer science) #Stigma (botany) #Tuberculosis #cond-mat.dis-nn #math-ph #math.MP #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.1186/2190-8567-2-12
published as The Journal of Mathematical Neuroscience 2012, 2:12 · 22 pages, no figures and 120 equations
openalex publication_date 2008/01/01 · arxiv created 2012/01/31 · arxiv updated 2014/09/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11
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.