Crisis (dynamical systems)

In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied.

[1][2] This global bifurcation occurs when a chaotic attractor comes into contact with an unstable periodic orbit or its stable manifold.

Grebogi, Ott, Romeiras, and Yorke distinguished between three types of crises:[4] Note that the reverse case (sudden appearance, shrinking or splitting of attractors) can also occur.

[5] While crises are "sudden" as a parameter is varied, the dynamics of the system over time can show long transients before orbits leave the neighbourhood of the old attractor.

[6] There also exist systems where the divergence is stronger than a power law, so-called super-persistent chaotic transients.