Mathematical Neuroscience
Fall 1999
Carlo Laing
Bard Ermentrout
Monday & Wednesday 3:00 - 4:30 PM
Thackeray 704
Syllabus
- Introduction to neuroscience
- Where is the brain?
- Ions and equilibrium potentials
- Brief review of currents and synapses
- Introduction to dynamical systems
- Dynamics, phaseplanes etc
- XPP
- Classification of spiking models
- Hodgkin Huxley via bifurcation
- Spiking induced via homoclinic, saddle-node, hopf bifurcations
- Bursting cells: from bursting to beating
- Small networks
- synaptic interaction/gap junctions/alpha functions
- Integrate and fire: Bressloff/Gerstner/Chow
- Weak coupling/averaging/adjoint!
- Canonical models
- Slow coupling
- singular perturbation
- Terman/Rubin analysis of coupled oscillators
- Fast Threshold Modulation
- Big Networks
- derivation
- reduction
- Wilson Cowan
- Hopfield theory - Lyapunov function
- Line attractors?
- Cohen-Grossberg theorem
- Spatial Patterns: bumps waves etc