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Thursdays 10-12am Course room: MAR 5.060

This course provides basic and advanced knowledge about the mathematical modeling, analysis and numerical simulation of biological neural networks. Specific topics addressed are: spiking neuron models, coupling of neurons, cooperative phenomena in neural networks, mean-field limits (strong and weak coupling) and continuum limits of neural networks (neural field equations for perception), associative memory and attractor dynamics (Hopfield model), competition models of decision making, synaptic plasticity

Learning outcomes:

Participants will learn basic and advanced concepts, their biological foundations and standard models in Computational Neuroscience, in order to model and analyze complex neural processes in brain networks. By the end of the course, they will be able to:

  • develop simplified models by separation of time scales
  • analyze networks in the mean-field limit
  • formalize biological facts into mathematical models
  • formulate stochastic models for biological phenomena
  • simulate network models and evaluate the statistics of simulation output

Literatur:

  • Gerstner, Kistler, Naud, Pansinski: Neuronal Dynamics, Cambridge Univ. Press 2014
  • Ermentrout, Terman: Foundations of Mathematical Neuroscience, Springer 2010
  • Dayan, Abbott: Theoretical Neuroscience, MIT Press, 2005