Description
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 Plotsuperimposed(use hold on command in MATLAB)
(b) Plot V(t) vs t and W(t) vs tand also show the trajectory on the phase plane for the both cases
(i) V(0) < a and ω (0)= 0 (ii) V(0) > a and ω (0)= 0
Case 2: Choose some current valueI1<Iext< I2 where it exhibit oscillations. Find the values of I1 and I2. (a) Draw a Phase Plot for some sample value ofIext (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 someIext> I2
(a) Draw a Phase Plot for some sample value of Iext
(b) Show that the fixed point is stablei.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:Fine suitable values of Iextand (b/r) such that the graph looks as phase plot shown as below.
(a) Redraw the Phase plot
(b) Show suitability of P1, P2, P3
(c) Plot V(t) vs t and W(t) vs t
Do not share your assignments with each other. Discussions are permitted but the code and the final report must be an individual effort. Please feel free to mail the group any doubts.
Submission Instructions
Enclose all your programs, plots and report in a single zip folder
Submit a compressed zip or tar file named as _A2.zip to any one of the following address. Please note do not drop your assignment on to the group.
anila.gundavarapu@gmail.com or bhadra.edu@gmail.com
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