MATLAB

use matlab to implement, then solve questions by hand please

Consider the modified FitzHugh-Nagumo equations, where p is a parameter

1. Make a sketch of the nullclines, indicating how the nullclines change if p changes. Use parameters =0.01, k=4, and a=0.2.
2. Determine the fixed point of the system as a function of p.
3. Compute the Jacobian of the system, evaluate it at the fixed point and determine the eigenvalues. The eigenvalues should be a function of p (and of p only).
4. For which value(s) of p are there bifurcations in the systems? Why?
5. Plot nullclines for p before, at, and after the bifurcations (where p is increasing).
6. Plot a few sample trajectories for p before, at, and after the bifurcations.

du/dt = U-P du/dt = U-P