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.
The relevant system of equations is
containing the empirical parameters , , and . Plots of variables , , and as functions of time appear at the bottom.
 A. Shilnikov and D. Turaev, "Blue-Sky Catastrophe," Scholarpedia, 2(8):1889, 2007. www.scholarpedia.org/article/Blue-sky_catastrophe.
 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.
 T. Vialar, Complex and Chaotic Nonlinear Dynamics, Berlin: Springer, 2009.