Global bifurcations occur when 'larger' invariant sets, such as periodic orbits, collide with equilibria. Saddle-node bifurcations may be associated with hysteresis loops and catastrophes. These situations are called perestroika (), bifurcations or catastrophes. The mapping of vascular bifurcations is one of the basic steps in biometric identification. A series of period-halving bifurcations leads the system from chaos to order. Feigenbaum has studied the logistic family and looked at the sequence of Period doubling bifurcations. Some bifurcations can lead to very complicated structures in phase space. Analysis of parameter continuation can lead to more insights about stable/critical point bifurcations. This is due to bifurcations, which cause a drop in pressure. He is editor of "World Futures" and for the "International Journal of Bifurcations and Chaos". Bifurcations and trifurcations occurs in 50% and 25% of the cases respectively. The predictions of the Novak-Tyson model are generic to all saddle-node bifurcations. Normal forms are often used for determining local bifurcations in a system.