I have a qustion about bifucation diagrams in the book they use the DE: dy/dt= y*(a-y^2)(adsbygoogle = window.adsbygoogle || []).push({});

the critical points for, a<0: dne a=0:y=0 and a>0: y=0,+-sqrt(a)

then they ploted critical points as a function of a in the ay plane and the equation of the graph looks like a=y^2 and the graph looks like a normal x=y^2 graph except that everything below y=0 is dashed and everything above is solid line. Is this because above a=0 the DE is stable and below a=0 it is unstable? also if this is the case, would for other functions as well where you just plot the function of a and dash the parts of the graph that are unstable?

thanks

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# Homework Help: Bifucation diagram

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