33 Pages
English

Mathematical Institute and OCCAM University of Oxford

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Niveau: Supérieur, Master
On the master equation approach to stochastic neurodynamics Paul C Bressloff Mathematical Institute and OCCAM, University of Oxford January 18, 2010 Paul C Bressloff On the master equation approach to stochastic neurodynamics

  • wilson-cowan equations

  • master equation

  • nk

  • homogeneous networks labelled

  • state transition

  • transition rate


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OnthemasterequationapproachtostochasticneurodynamicsPaulCBressloffMathematicalInstituteandOCCAM,UniversityofOxfordaPluJanuary18,2010CrBselsonOhteamtsreqeauitnoparpaohcottsohcsaitcenruoydanimsc
raPt.IMasterequationluaPCBressloffnOtehmasterequationapproachototschasticoruendynamics
MasterequationIConsiderMhomogeneousnetworkslabelledk=1,...M,eachcontainingNidenticalneuronsAssumethateachneuroncanbeinoneoftwostates,quiescentoractiveie.intheprocessofgeneratinganactionpotential.Supposethatintheinterval[t,tt)therearenk(t)activeneuronsinthekthpopulationDefinepopulationactivityintermsofthefractionofactiveneuronsaccordingtoaPluCrBu(N)(t)=nk(t).kNselsonOhteamtsreqeauitnoparpaohcottsohcsaitcenruoydanimsc