The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v (t) obeys the differential equation dv dt = - v[v2 - (1 + a) v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0) ? (Enter your answers as a comma-separated list.) v

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Physics

Alivia Stephens

30 March, 08:31

The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v (t) obeys the differential equation dv dt = - v[v2 - (1 + a) v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0) ? (Enter your answers as a comma-separated list.) v

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Brenden Whitehead · Answer 1

v = 0, 1, a

Explanation:

dv/dt = v (v² - (1 + a) v + a)

When dv/dt = 0

=> 0 = v (v² - (1 + a) v + a)

=> v = 0 and (v² - (1 + a) v + a) = 0

Open up the bracket:

v² - v - av + a = 0

v (v - 1) - a (v - 1) = 0

(v - a) (v - 1) = 0

=> v = a and v = 1

Hence, the values of v for which dv/dt can be 0 are v = 0, 1, a.