# Find all bifurcation points (ODEs)

1. Jul 31, 2012

### anonymity

I'm at a loss on this question...my troubles seem to be algebraic or that i'm simply missing something.

x' = $\mu$ - x2 +4x4

my method for these questions has basically been to do everything required to draw bifurcation diagram bar drawing the actual diagram itself (ie, find equilibria, what values of mu create/destroy them, and the intervals of stability). Here solving for x in terms of the parameter mu has been a challenge. I've been trying to think of what it means to have mu as a function of x and what that can do for me, but so far I have nothing.

Is this the correct method, or am I making this harder than it needs to be? I'm taking the course independent as an independent study, so every once in a while I cant help but wonder.

If I am doing it right can someone give me a hint here? -.-

2. Jul 31, 2012

### Dick

If you want to find the equilibrium points you want to solve mu-x^2+4x^4=0, yes? That's not too hard. Substitute u=x^2 first. Now you have a quadratic in u. Solve it for u and then find x.

Last edited: Jul 31, 2012