Examples of Pitchfork Bifurcation in nature?

I was just wondering if anyone had some nice examples of pitchfork bifurcation in nature! For Hopf Bifurcations, for me the classical example is cylinder flow. What is the same for a pitchfork bifurcation?

Best wishes,

Catherine

Solution 1:

One instance is the existence of a critical temperature $T_c$ for self-magnetization (Curie temperature). Above $T_c$, there is no macroscopic magnetization ; the orientations of the spins is somewhat homogeneous. Under $T_c$, the homogeneous configuration is unstable, and the spins will align (at least at a mesoscopic level), to simplify, either up or down.

This phenomenon can be studied e.g. in the relatively simple mean-field Ising-Curie-Weiss model, where a pitchfork bifurcation occurs at a critical temperature. See for instance this chapter, Equation (2.12) and figure below.