# Sketch a bifurcation diagram

1. Sep 24, 2011

### squenshl

1. The problem statement, all variables and given/known data
Consider the ODE
x' = $\mu$x - x2 + x4
where x $\in$ R and $\mu$ $\in$ R is a parameter.
Find and identify all bifurcation points for this equation. Sketch a bifurcation diagram, showing clearly the stability of all equilibria and the location of the bifurcation points.
You may identify any bifurcations you find from the bifurcation diagram but you must also check the conditions from any bifurcation theorems.

2. Relevant equations

3. The attempt at a solution
Is it just the same-old way.
1) Find equilibria and the Jacobian and from the Jacobian find stability of equilbria etc and if not what do I do.

2. Sep 27, 2011

### squenshl

Re: Bifurcation

x = 0 is an equilibria but how do I find the others.

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