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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$\frac{d v}{d t}=-v\left[v^{2}-(1+a) v+a\right]$where $a$ is a constant and $0< a <1$(a) For what values of $v$ is $v$ unchanging (that is, $d v / d t=0 ) ?$(b) For what values of $v$ is $v$ increasing?(c) For what values of $v$ is $v$ decreasing?

$$v \text { is decreasing when } v \in(0, a) \cup(1, \infty)$$

Calculus 2 / BC

Chapter 7

Differential Equations

Section 1

Modeling with Differential Equations

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All right. So for this question, once you solve for DVD teeth by taking the regular derivative, we can see the DVD T is equal to zero on Lee when he is equal to zero. V is equal to one on the is equal to a. We also can tell that he's increasing when V is between negative infinity to zero on dhe. And so that's how you end a change between when movies between a while, these decreasing so we can leave all this as increasing. And this is decreasing. These decreasing when he's between zero and a or when V is between one and infinity.

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