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Contents 1 Applications of Dynamical Systems in Neurophysiology and Neuroscience 1.1 Tentative breakdown of Lectures 1.2 Possible Laboratory Projects/Pracs 1.3 Refs

Applications of Dynamical Systems in Neurophysiology and Neuroscience

Contributors: David Liley, [1] Federico Frascoli, [2]

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Tentative breakdown of Lectures

Lecture 1 - Introductory remarks on Dynamical Activities in Neurobiology

1. Dynamics phenomena in neurobiology (with a emphasis on multiple temporal and spatial scales)
   1. Action Potentials and Excitability (3 types)
   2. EEG/ECoG
   3. BOLD, etc
2. Early attempts to describe these phenomena
3. Levels of models: micro, meso and macro
4. Microscopic Neuronal modeling and the Hodgkin–Huxley (HH) model: their development from experiment.

Lecture 2 - Fundamental Models of Neuronal Activity

1. Synthesis of HH equations
2. Basic Features and analysis of HH equations
3. 1-D reductions of HH equations and approximations
4. 2-D planar reductions of HH equations and approximations (FitzHugh-Nagumo)
5. Other conductance-based models:
   1. minimal (ie capable of spiking) conductance-based models and planar reductions
   2. Morris-Lecar model
   3. Rose-Hindmarsh neuron
6. Bursting, Chaos and other dynamics

Lecture 3 - Dynamics of Networks of coupled neuronal models

1. Overview of Anatomy of important studies of physiological interest - cortex, thalamus (main ones)
2. Connectivity
   1. General topology
   2. Synaptic connectivity and EPSPs
3. Coupled spiking networks
   1. Oscillation and Synchrony (needs more detail)
   2. CPGs, sleeps spindles (TRN and RN) "a la Destexhe" (1994)

Lecture 4 - Meso- and Macroscopic Neuronal Modelling

1. Some basic neuroanatomy
2. Classical macroscopic models and solutions
   1. Wilson and Cowan
   2. Amari (bump solutions ?)
3. Modelling electrorhytmogenesis in the EEG
   1. Freeman and K-sets
   2. Lopes da Silva
   3. Nunez, Jirsa and Haken
   4. Robinson et al.
   5. Liley et al.

Possible Laboratory Projects/Pracs

Lab 1

1. HH equations and quasi-static reductions (using Matlab, XPPAUT)
2. Illustration of some codimension 1 and 2 bifurcations for equilibria and homoclinics (XPPAUT, MATCONT)

Lab 2

1. Coupled Networks of excitable elements: Central Pattern Generators (CPG) and sleep-spindels
2. Simulation and Analysis of Mean Field Models, with a taste of Chaos (Wilson and Cowan, Liley et al.)

Refs

• ANU Physics Summer Schools page

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