Real brains aren't one neuron — they're populations that push and pull on each other. We'll model two: an excitatory group (gas pedal 🟦) and an inhibitory group (brake 🟥). This is a simplified Wilson–Cowan model.

Each population's firing rate changes based on the other's rate. Two coupled differential equations (with internal connections switched off for now):

τ_E·dr_E/dt = w_EI·r_I τ_I·dr_I/dt = w_IE·r_E

r_E, r_I = excitatory / inhibitory firing rates. The w's are connection strengths between the groups.

The Euler trick doesn't change one bit — it's still Future = current + step × dynamics. The only new thing: there are two variables, so we update both inside the same loop, because each depends on the other's current value.

Excitation ramps inhibition up; inhibition drags excitation down; which lets inhibition fall; which lets excitation rise again… That back-and-forth is exactly what produces oscillations — a rhythm, like brain waves. You'll see it in two lessons.