Single Neuron Models - II
Single Neuron Models - II
This lesson continues from the previous lectures, providing introduction to stability analysis of neural models.
Topics covered in this lesson
- Phase plane solutions
- Eigenvalue examples
- Saddle point
- Stable and unstable manifolds
- Stable and unstable nodes
- Revisiting the predator-prey example
- Nullclines
- Phase portrait for the predator-prey equation
- Phase portrait for a neuron, at rest and with current
- Bifurcation diagram
- Limit cycles
- Hopf bifurcation theorem
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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