_____________________________________________________________________________________
Simulate the two variable FitzHugh-Nagumo neuron model using the following equations:
where a=0.5; choose b, r = 0.1)
Use single forward Euler Integration
dv/dt = Δv/ Δt
Δv(t) = v(t+1) - v(t) = [fv(t) - w(t) + Iext(t)]* Δt given v(0) --> v(Δt ) --> v(2* Δt ) -->....
Case 1: Iext = 0
(a) Draw a Phase Plot superimposed (use hold on command in MATLAB)
(b) Plot V(t) vs t and W(t) vs t and also show the trajectory on the phase plane for the both cases
(i) V(0) < a and W (0)= 0
(ii) V(0) > a and W (0)= 0
Case 2: Choose some current value I1 < Iext < I2 where it exhibit oscillations. Find the values of I1 and I2.
(a) Draw a Phase Plot for some sample value of Iext
(b) Show that the fixed point is unstable i.e., for a small perturbation there is a no return to the fixed point (show the trajectory on the phase plane) – also show limit cycle on the phase plane
(c) Plot V(t) vs t and W(t) vs t
Case 3: Choose some Iext > I2
(a) Draw a Phase Plot for some sample value of Iext
(b) Show that the fixed point is stable i.e., for a small perturbation there is a return to the fixed point (show the trajectory on the phase plane)
(c) Plot V(t) vs t and W(t) vs t
Case 4: Find suitable values of Iext and (b/r) such that the graph looks as phase plot shown as below.
(a) Redraw the Phase plot
(b) Show stability of P1, P2, P3
(c) Plot V(t) vs t and W(t) vs t
Submission Instructions
Enclose all your programs, plots and report in a single zip folder
Please submit a compressed zip or tar file named as <ROLLNO>_A2.zip by sending it to one of the TAs via email (email IDs given below). Report should be very clear and all assumptions should be clearly highlighted.
Email IDs of the TAs
sayanghoshbme@gmail.com
sundarielango95@gmail.com
