Chapter 9.1, Problem 10E

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

$\frac{dv}{dt}=-v[v^2-(1+a)v+a]$

where a is a positive constant such that 0 < a < 1.

1. (a) For what values of v is v unchanging (that is, dv/dt = 0)?
2. (b) For what values of v is v increasing?
3. (c) For what values of v is v decreasing?