## richyw 3 years ago Bifurcation diagrams. No idea what i'm doing... The differential equation depends on a parameter $$a\in\mathbb{R}$$. Find the equilibrium points and determine whether they are source, sink or neither and sketch the bifurcation diagram. $x'(t)=x^3-2ax^2+4x$ where $$a\geq 0$$

1. abb0t

If I remember correctly, to find the equilibrium points, find the zero's. So factor out an x... $x(x^2-2ax+4)=0$

2. abb0t

plug in the equilibrium points for f'. and If f is less than the equilibrium points then it's a source, and sinks if it's greater than equilibrium point.

3. richyw

ok what I am struggling with is how to split it up. like for some values of a there are a different amount of equlibrium points. are there any resources that just explain what is going on? i'm at my wits end with Hirsch, Differential equations. There isn't even a solution manual

4. anonymous

I found something that may be helpful

5. anonymous
6. anonymous

Go to page 53 Example 31