richyw
  • 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 \(a\geq 0\)
Mathematics
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richyw
  • 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 \(a\geq 0\)
Mathematics
jamiebookeater
  • jamiebookeater
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abb0t
  • abb0t
If I remember correctly, to find the equilibrium points, find the zero's. So factor out an x... \[x(x^2-2ax+4)=0\]
abb0t
  • 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.
richyw
  • 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

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swissgirl
  • swissgirl
I found something that may be helpful
swissgirl
  • swissgirl
http://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CEIQFjAC&url=http%3A%2F%2Fwww.math.utah.edu%2F~gustafso%2F2250phaseline.pdf&ei=HDb-UPrbO8Xd0QGDyICADA&usg=AFQjCNGFuGaShSKXuMS06cs1UZwS7v94Qw&sig2=lRJCHNClHKGY4Pa6Aa-yLQ&bvm=bv.41248874,d.dmQ
swissgirl
  • swissgirl
Go to page 53 Example 31

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