Bifurcation theory

Bifurcation theory is a way of understanding the behavior of a system based on how it responds to changes in its environment. Imagine a river flowing down a mountain. A bifurcation is like a point at which that river splits into two different parts. By looking at the environment at each of these points, like the shape of the land and the amount of water in the river, we can understand why the river has chosen to split into two different directions. In mathematics, bifurcation theory helps us understand how equations can have different solutions depending on the different values of their variables.