Computational_Neuroscience

Semester project: The first part was designed to numerically simulate the Moris Lecar Equations (MLE) and perform phase plane analysis. In the second part the project builds on the MLE to simulate Hodgkin Huxley (HH) equations and then simulations of other HH type models of neurons.

phase-plane plot with nullclines, equilibrium points, and arrows:

Phase with different phi ( action potential in MLE)

Simulate depolarizing current pulses of various amplitudes by setting the voltage initial condition to a succession of values positive to the resting potential while starting w at the equilibrium point.

Action potentials are usually thought to have thresholds. Does the MLE with the given set of parameters have a threshold depolarization?

Plot of phase-plane trajectories for values of initial depolarization that do and do not produce action potentials.

Plot of the three trajectories on a phase plane:

1. Set the initial conditions to the equilibrium point used above, appropriate for Iext=0;
2. Set the initial conditions to the equilibrium point when Iext=86 μA/cm2;
3. Set the initial conditions off the equilibrium point for Iext=86 μA/cm2, say at (-27.9, 0.17).