- 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 andlength of the orbit approaching infinity as the control parameter approaches a finite bifurcation value, but with the orbit still remaining within abounded part of thephase space , and without loss ofstability before the bifurcation point. In other words, the orbit "vanishes into the blue sky".The bifurcation has found application in, amongst other places,
slow-fast model s ofcomputational neuroscience . The possibility of the phenomenon was raised byDavid Ruelle andFloris Takens in 1971, and explored byR.L. Devaney and others in the following decade. More compelling analysis was not performed until the 1990's.This bifurcation has also been found in the context of
fluid dynamics , namely in double-diffusive convection of a smallPrandtl number fluid. Double diffusive convection occurs when convection of the fluid is driven by both thermal and concentration gradients, and the temperature and concentration diffusivities take different values. The bifurcation is found in an orbit that is born in a global saddle-loop bifurcation, becomes chaotic in a period doubling cascade, and disappears in the blue sky catastrophe.References
* [http://www.scholarpedia.org/article/Blue-Sky_Catastrophe Blue Sky Catastrophe] article in
Scholarpedia
* [http://www.mathstat.gsu.edu/%7Ematals/ Andrey Shilnikov] - one of the researchers of the phenomenon.
* [http://prola.aps.org/abstract/PRL/v92/i23/e234501 E. Meca et al. Phys. Rev. Lett. 92, 234501 (2004)] - Blue Sky Catastrophe in fluid dynamics.
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