Bifurcation and Stability of Equilibria

[bartieshaw]

When determining the stability of the equilibria (or, critical points) for our bifurcation diagrams, we have been shown to use phase line diagrams.

I understand that if the function is moving away from the equilibria on either side than it is unstable, and i know that if the function is moving toward the equilibria on either side it is stable.

But how do you determine if the equilibria is asymptotically stable or just stable (or are these the same things?)?

And what does it mean when the function is moving in the same direction on either side of the equilibria. I think my lecturer called this a shunt, is this represented on a bifurcation diagram?

cheers

bart

 

[fresh_42]

Have a look into
https://www.math.utah.edu/~gustafso/2250phaseline.pdf