A bifurcation refers to a division or branching into two parts or categories. In mathematics, it often describes a change in the number or stability of equilibria in a system as a parameter varies. In other contexts, it can refer to a fork in a road or a division of pathways, often symbolizing a choice or decision point.
Examples:
Mathematics: In dynamical systems, the bifurcation of a fixed point can occur when a parameter crosses a critical value, leading to the emergence of new equilibria.
Biology: In evolutionary biology, bifurcation can refer to speciation events where a single species diverges into two distinct species.
Roads: A bifurcation occurs at a junction where a single road splits into two different directions, requiring drivers to make a choice.
Cases:
Pitchfork Bifurcation: A common type in which a single stable equilibrium point becomes two stable points and one unstable point as a parameter changes.
Transcritical Bifurcation: Occurs when two equilibrium points exchange stability as parameters vary, often seen in ecological models.
