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Assignment 2 FitzHugh-Nagumo neuron model

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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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