138 Pages
English
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Simulations of a neuron network model in the olfactory system [Elektronische Ressource] / vorgelegt von Carmen R. Ellsässer

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138 Pages
English

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INAUGURAL - DISSERTATIONzurErlangung der DoktorwürdederNaturwissenschaftlich-Mathematischen GesamtfakultätderRuprecht-Karls-UniversitätHeidelbergvorgelegt vonDipl.-Math. Carmen R. Ellsässeraus HeidelbergTag der mündlichen Prüfung: 30.10.2008Simulations of a Neuron Network Modelin the Olfactory System1. Gutachter: Prof. Dr. Dr. h.c. mult. Willi Jäger2. Gutachter: Prof. Dr. Peter BastianiiAbstractInthisworkamodelfortheneuronnetworkintheolfactorybulbisdeveloped. Themodelincludesmitralandgranulecells,modeledaspointneuronswithintegrate-and-firedynamics. Theactivityofthe network model is simulated and numerically analyzed using so-called equation-free techniques.Thesetechniquesallowtoinvestigatethemacroscopic,coarsebehaviorofhighdimensionalsystemswithoutderivingclosedlow-dimensionalequations. Theequation-freesimulationtoolsareadaptedtotheneedsofinvestigatingthecoarsebehavioroftheolfactorybulbnetworkmodelhere: equation-free Newton’s method, parameter studies and methods for traveling waves are introduced. Byinterpreting the equation-free time-stepping scheme as an one-step method it is proven that thenumerical solution converges to the analytical solution as the length of the time step tends to zero.Point neurons are sometimes not sufficient, i.e. the spatial expansion of a neuron has tobe considered to compare simulation results to results of imaging experiments.

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Published 01 January 2009
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Language English
Document size 11 MB

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