Bifurcation Analysis for the ODE x' = \mux - x2 + x4

[squenshl]

Homework Statement

Consider the ODE
x' = \mux - 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.

Homework Equations

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.

 

[squenshl]

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