Gavrilov-Shilnikov Model

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The Gavrilov–Shilnikov model exhibits a bifurcation known as the "blue-sky catastrophe", which is the last of the seven known bifurcations of a periodic orbit. This catastrophe creates a stable periodic orbit whose length and period increase without bound. Some applications include models for neuron activity and the operation of jet engines.

Contributed by: Enrique Zeleny (August 2012)
Open content licensed under CC BY-NC-SA



The relevant system of equations is

containing the empirical parameters , , and . Plots of variables , , and as functions of time appear at the bottom.


[1] A. Shilnikov and D. Turaev, "Blue-Sky Catastrophe," Scholarpedia, 2(8):1889, 2007.

[2] N. Gavrilov and A. Shilnikov, "Example of a Blue Sky Catastrophe," Methods of Qualitative Theory of Differential Equations and Related Topics, American Mathematical Society Translations, 2(200), (L. Lerman, G. Polotovskii, and L. Shilnikov, eds.), Providence, RI: American Mathematical Society, 2000 pp. 99–105.

[3] T. Vialar, Complex and Chaotic Nonlinear Dynamics, Berlin: Springer, 2009.

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