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30 May, 08:43

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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  1. 30 May, 08:44
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    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.
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