Question

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

Answer 1

Answer:

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.