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Single neuron models - I

Difficulty level

Introduction to stability analysis of neural models

Topics covered in this lesson
  1. Basic introduction to neurons, ionic conductances, synapses and neurotransmitters
  2. Dale's principle
  3. Equivalent circuit model for a membrane
  4. Nernst equation
  5. The action potential
  6. Introduction to the Hodgkin-Huxley model
  7. Steady-state I-V curve
  8. Equilibrium points
  9. Oscillations and stability
  10. Principle of linearised stability
  11. Example: predator-prey dynamics
  12. Eigenvalues and stability
  13. Morris-Lecar simplified 2D model of excitation
  14. Stability analysis of the Morris-Lecar model

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 neurosciences. Knowledge of differential equations. Some familiarity with dynamical systems concepts and/or linear algebra (stability, equilibrium, matrices, finding eigenvalues).