1. The problem statement, all variables and given/known data As in title. 2. Relevant 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. 3. 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?