Course content / topics
The activity patterns of neurons result from complex dynamic interactions between many neurons, or compartments of individual neurons in the nervous system. Neural models try to capture the fundamental properties of such dynamical processes and, making them accessible for mathematical analysis and computer simulation. This course treats the basic biophysics of the signal generation and transmission in neurons and discusses how the underlying physical and physiological phenomena can be approximated by mathematical models. Typically, such models can be characterized as nonlinear dynamical systems. The course provides a systematic introduction in the mathematical theory of linear and nonlinear dynamical systems, and demonstrates how these mathematical methods can be applied to analyze fundamental properties of neurons and neural networks. This framework provides a deeper understanding of fundamental phenomena neural structures, such as passive and active signal propagation, active pattern formation and decision, and basic properties of oscillations and synchronization in neural systems.
Course Schedule & Topics
Participants will learn to develop biophysically plausible neural models with different levels of abstraction. The will learn the fundamental mathematical techniques to implements simulations of such models numerically, and to analyze properties of simplified models, applying different techniques from analysis and the theory of differential equations. In addition, students should develop a deeper theoretical understanding of several central phenomena in neurons and cortical and subcortical networks, which are treated phenomenologically in the neurophysiology lecture.
Basic knowledge of analysis and linear algebra. Basic programming skills (MATLAB or Python). Elementary knowledge about neurons and the structure of the nervous system (as provided by the courses in Functional Neuronatomy and Neurophysiology).
Dayan, P. Abbott, L.F. (2001 / 2005) Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press, Cambridge, MA. Parts II and III, Chapters 5-8, 10.
Sterratt, D., Graham, B, Gillies, A., Willshaw, D. (2011) Principles of Computational Modelling in Neuroscience. Cambridge University Press, UK. Chapters 1-5, 8.
Additional literature will be provided during the lecture.