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Electroencephalograms (EEGs)

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Solve (2) explicitly for V(x, t). By choosing a specific test function Qa, show that
(2) indeed describes a lagged response.
ii. Physiologists measure re ≈ 0.084m, ri ≈ 10−4m, and v ≈ 9ms−1 in humans. Explain
why this implies Φi ≈ Qi.
iii. Show that the cortex supports three uniform equilibria if
in the regime aee ≫ aei and aie ≫ aii; otherwise, it supports one equilibrium.
iv. Now perturb the uniform equilibria in part (iii) assuming an infinitely extended
cortex, such that the perturbations are proportional to exp(−iωt + ik ⋅ x).
a) Derive the dispersion relation
v.
where G = g aee(dQe/dVe)eq is evaluated in the equilibrium state.
b) G is called the gain. What does it signify physically?
a) Show analytically or numerically that the cortex is unstable for
✓
@2
@t2 + 2"e
@
@t
+ "2
e − v2r2
â—†

Electroencephalograms (EEGs)

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