Dynamical Systems in Neuroscience.pdf

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1、EugeneM.IzhikevichTheNeurosciencesInstituteDynamicalSystemsinNeuroscience:TheGeometryofExcitabilityandBurstingJuly4,2005TheMITPressContentsPrefaceix1Introduction11.1Neurons...................................11.1.1Whatisaspike?..........................21.1.2Whereisthethreshold?....................

2、..31.1.3Whyareneuronsdifferentandwhydowecare?.........61.1.4Buildingmodels...........................61.2DynamicalSystems.............................71.2.1Phaseportraits...........................81.2.2Bifurcations.............................101.2.3Hodgkinclassification........................141.

3、2.4Neuro-computationalproperties..................161.2.5Buildingmodels(revisited).....................20SummaryandBibliographicalNotes......................202ElectrophysiologyofNeurons252.1Ions.....................................252.1.1Nernstpotential...........................262.1.2Ioniccurre

4、ntsandconductances..................272.1.3Equivalentcircuit..........................282.1.4Restingpotentialandinputresistance..............292.1.5Voltage-clampandI-Vrelation..................302.2Conductances................................332.2.1Voltage-gatedchannels.......................332.2

5、.2Activationofpersistentcurrents..................352.2.3Inactivationoftransientcurrents.................362.2.4Hyperpolarization-activatedchannels...............372.3Hodgkin-HuxleyModel...........................372.3.1Hodgkin-Huxleyequations.....................382.3.2ActionPotential............

6、..............392.3.3Propagationoftheactionpotentials................432.3.4Dendriticcompartments......................43iii2.3.5Summaryofvoltage-gatedcurrents................45SummaryandBibliographicalNotes......................49Exercises......................................513One-DimensionalSy

7、stems553.1ElectrophysiologicalExamples.......................553.1.1I-Vrelationsanddynamics.....................563.1.2Leak+instantaneousINa,p.....................573.2DynamicalSystems............................