Wednesday, March 24, 2010

Dear Hopf Bifurcation Theory -

A plot of the trajectory Lorenz system
I’ve been trying to get to know you better (I’m sure you remember when Logan introduced us). Let me get this straight: we start with two steady states. Something is orbiting between these two potentials, but it has an unstable relationship with both. It will slowly attract to one of the fixed points, orbit closer and closer, and then, unpredictably and chaotically, it will shoot out at another trajectory and orbit around the other fixed state. It is called “bifurcation” because it never penetrates either steady state; it oscillates between the two. And there is a limit cycle so the orbit can be mathematically traced, based on where you are, where you should go next, and then, you know, time. I could be wrong, but I think that might be it. I liked meeting you because Logan kept using great words like turbulent and equilibrium. We understand metaphor, but we just don’t talk like that in the Humanities. I wish we did.


1 comment:

I try to respond to comments if I have your email :)