**The Single Neuron**Nonlinear integrate-and-fire models

- Models of the single neuron.
- Mathematical reductions and canonical models.
- Analysis of excitable and oscillatory behaviour using dynamical systems techniques.
- Phase response curves and isochronal coordinates.
- Mode-locking to periodic stimuli.

**Neural Systems**- Models of the synapse and dendrite.
- Return maps for pulse-coupled oscillators.
- Networks of interacting phase oscillators.
- Rhythm generation in biological central pattern generators.
- Travelling waves in neural systems.
- Firing rate models, population models and mean field descriptions for large networks.
- Pattern formation in neural systems and drug-induced visual hallucinations.

Ermentrout, G. B. and Terman, D. H. (2010). Mathematical Foundations of Neuroscience, Springer. |

Wilson, H. (1999). Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience, Oxford University Press. |

Hoppensteadt F. C. and Izhikevich, E. (1997) Weakly connected neural networks, Springer. |

Izhikevich, E (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting,The MIT Press. |

Koch, C. (1999). The Biophysics of Computation, Oxford University Press. |

Keener, J. and Sneyd, S. (1999) Mathematical Physiology, Springer. |

Murray, J. D. (1993) Mathematical Biology (2nd edition), Springer-Verlag. |

Nicholls, J. G., Martin, A. R., Wallace, B. G. and Fuchs, P. A. (2001) From Neuron to Brain (fourth edition) Sinauer |

Strogatz, S. (1994). Nonlinear Dynamics and Chaos. Addison-Wesley. |

- Problem sheet 1
- Problem sheet 2
- Problem sheet 3
- Problem sheet 4
- Problem sheet 5
- Problem sheet 6
- Problem sheet 7
- Problem sheet 8

Measurement of current-voltage relations in the membrane of the giant axon of Loligo

Full text in PDF format.

Hodgkin, A. L., and Huxley, A. F. (1952a).

Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo

*J. Physiol.* 116: 449-472

Full text in PDF format.

Hodgkin, A. L., and Huxley, A. F. (1952b).

The components of membrane conductance in the giant axon of Loligo.

*J. Physiol.* 116: 473-496

Full text in PDF format.

Hodgkin, A. L., and Huxley, A. F. (1952c).

The dual effect of membrane potential on sodium conductance in the giant axon of Loligo

*J. Physiol.* 116: 497-606

Full text in PDF format.

Hodgkin A.L., and Huxley A.F. (1952d).

A quantative description of membrane current and its application to conduction and excitation in nerve

*J. Physiol.* 117: 500-544

Full text in PDF format.

S Coombes Jan 2008

`stephen.coombes@nottingham.ac.uk`