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richyw
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 \(a\geq 0\)
If I remember correctly, to find the equilibrium points, find the zero's. So factor out an x... \[x(x^2-2ax+4)=0\]
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.
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
I found something that may be helpful
Go to page 53 Example 31