To the first page

Catastrophes

We see the function f(x) = x4-x2-c x, where c varies between -1 and 1. The movie starts when c=0 then goes to 1, returns back to 0 goes to -1 and back to 0. The system always choses the nearest local minimum as mandated by Delay assumption of catastrophe theory. Parameters (=time values here), where a local minimum disappears, is called a catastrophe. To the right we see the "bifurcation diagram" in real time and where the parameter c is. The background song is "Head over Heals" by Abba is chosen because of its meaning "upside down".