Blue sky catastrophe

The blue sky catastrophe is a type of bifurcation of a periodic orbit. In other words, it describes a sort of behaviour stable solutions of a set of differential equations can undergo as the equations are gradually changed. This type of bifurcation is characterised by both the period and length of the orbit approaching infinity as the control parameter approaches a finite bifurcation value, but with the orbit still remaining within a part of the phase space, and without loss of stability before the bifurcation point. In other words, the orbit vanishes into the blue sky.