[Python] FitzHugh–Nagumo model output not resembling what is shown on Wikipedia

First off, I just want to mention that I am a biology researcher not trained in differential equations or dynamical systems. I am doing this as an exercise to get a bit of intuitive understanding of dynamical systems in Neuroscience.

I am trying to implement the FitzHugh-Nagumo model as it is shown in the linked Wikipedia article. This is a dynamical model of neuronal excitability, and a simplified version of the comprehensive Hodgkin & Huxley model.

First, I wrote some code for calculating the dynamic variables v' and w':

def dv(V, W, R, I):
return V - ((V**3)/3) - W + (R*I)

def dw(V, W, a, b, tau):
return (V+a-(b*W))/tau


Next, I initialize some fixed parameters, identical to the ones given in the first two figures of the Wikipedia article.

## fixed params
a = 0.7
b = 0.8
tau = 12.5
R = 0.1
I = 0.5


Then, I set some initial conditions for the system. I picked an initial V to the right of the V nulcline and an initial W under the W nulcline. According to the phase portrait given in the article, this should generate oscillating spiking behavior.

## initial conditions
W = -0.5
V = 0


Finally, I wrote a simple iterative integrator to solve the equations. This is just a basic for loop, rather than an actual ODE solver, because right now I'm just trying to understand the basic intuition of dynamical systems.

## timescale
T = 200
dt = 0.01

# Initializing arrays to save the solution
fV = np.zeros(int(T/dt))
fW = np.zeros(int(T/dt))
fW[0] = W
fV[0] = V

# Integrate numerically via a for loop
for i in range(int((T/dt)-1)):
i = i+1

W+=dw(V, W, a, b, tau) * dt
V+=dv(V, W, R, I) * dt

fV=V
fW=W


Based on the parameters I entered into the model, I should get an oscillating output that looks like this, according to the Wikipedia article:



However, when I implement the code myself, I get an output that looks like this, lacking the oscillating behavior:



I am not sure what I'm doing wrong. I am not familiar with numerical integration techniques, so I'm wondering if there's something incorrect about the for loop approach. Otherwise, I checked the rest of my code for potential mistakes but couldn't find anything. Any help or insight would be much appreciated!

Thank you!

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