- #1

Jamin2112

- 986

- 12

## Homework Statement

As in title.

## Homework Equations

My book has a very shaky definition of what a bifurcation point. Basically, I need to play around with r and see how the system changes.

## The Attempt at a Solution

x' = 0 when x = 1/2 - r ± √((r-1/2)

^{2}- 2r)

d/dx (x') = 1/2 - 1/(x+1)

^{2}, so

d/dx (x') > 0 when -1 - √2 < x < -1 + √2, and d/dx (x') < 0 when x < - 1 - √2 or x > -1 + √2.

I'm trying to combine these to find the ranges of r that I need to look at. Any ideas?