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Single Neuron Models - II

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Difficulty level
Intermediate
Speaker
Type
Duration
1:25:38

Introduction to stability analysis of neural models

Topics covered in this lesson
  1. Phase plane solutions
  2. Eigenvalue examples
  3. Saddle point
  4. Stable and unstable manifolds
  5. Stable and unstable nodes
  6. Revisiting the predator-prey example
  7. Nullclines
  8. Phase portrait for the predator-prey equation
  9. Phase portrait for a neuron, at rest and with current
  10. Bifurcation diagram
  11. Limit cycles
  12. Hopf bifurcation theorem
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 neurosciences. Knowledge of differential equations. Some familiarity with dynamical systems concepts and/or linear algebra (stability, equilibrium, matrices, finding eigenvalues).

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