Pitchfork Bifurcation

A pitchfork bifurcation occurs in dynamical systems when a small change in a parameter causes a system's stable state to split into multiple states. Imagine a graph shaped like a pitchfork: as you vary the parameter, a single stable solution branches into two new solutions, one of which may be stable and the other unstable. This phenomenon explains how systems can suddenly shift from a single equilibrium to multiple possibilities, often leading to complex behaviors like sudden transitions or pattern formations in physical, biological, or engineering contexts.