Single Neuron Models - I
Single Neuron Models - I
This lesson gives an introduction to stability analysis of neural models.
Topics covered in this lesson
- Basic introduction to neurons, ionic conductances, synapses and neurotransmitters
- Dale's principle
- Equivalent circuit model for a membrane
- Nernst equation
- The action potential
- Introduction to the Hodgkin-Huxley model
- Steady-state I-V curve
- Equilibrium points
- Oscillations and stability
- Principle of linearised stability
- Example: predator-prey dynamics
- Eigenvalues and stability
- Morris-Lecar simplified 2D model of excitation
- Stability analysis of the Morris-Lecar model
External Links
Prerequisites
Some familiarity with the electrical properties of neurons, for instance the (longer) introductory lectures in Cellular Mechanisms of Brain Function or the (shorter) tutorial series on Basic Mathematics for Computational Neuroscience. Knowledge of differential equations. Some familiarity with dynamical systems concepts and/or linear algebra (stability, equilibrium, matrices, finding eigenvalues).
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