Bifurcations

Bifurcations are qualitative changes of the phase portrait of a dynamical system that are characterized by the creation or destruction of fixed points in the phase space. They can occur when values of system parameters are changed beyond a critical point, called bifurcation point. The parameters for which a bifurcation can be observed are called bifurcation or control parameters. Bifurcations can be displayed, by plotting the position of the fixed points of a system against a control parameter. This gives the so called bifurcation diagram.

Saddle-node/fold/turning-point bifurcation

Saddle-node bifurcations (or fold/turning point bifurcations) are the basic mechanism for fixed point creation and destruction. As a parameter is varied, two fixed points approach, collide and annihilate each other.