BT6270: Computational Neuroscience

Assignment 2

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General Instructions:

✓ The goal of this assignment is simulating and Understanding FitzHugh-Nagumo neuron

model taught in the class.

✓ This is an individual assignment.

✓ You may use MATLAB or PYTHON for your implementation.

✓ You have to turn in the well commented code along with a detailed report of the study.

✓ Your report should contain answers for all of the questions/cases asked below.

✓ Look at the end of the assignment for submission instructions.

✓ Submission deadline: 16

th

Simulate the two variable FitzHugh-Nagumo neuron model using the following equations:

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

where a=0.5; choose b, r = 0.1)

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.

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