# Critical points (will be a function of beta and delta)

1. Mar 8, 2012

### Rubik

1. The problem statement, all variables and given/known data

Find the critical points where $\alpha$ = 1.

dv/dt = v2 + $\alpha$v - u + $\delta$ [I will call this (1)]

du/dt = $\beta$v - u [call this (2)]

For what values of $\beta$ and $\delta$ are there no critical points?

2. Relevant equations

3. The attempt at a solution

So firstly I set (1) and (2) to = 0 and from (2) I get:
u = $\beta$v and now I subst. this back into (1)

0 = v2 + v(1 - $\beta$) + $\delta$

Now from the quadratic formula I have this

v = {-(1 - $\beta$) ± √[(1 - $\beta$)2 - 4$\delta$]}/2

Now here I am stuck and not sure how to simplify this or interpret this?