The Burke & Shaw system has been derived by Bill Burke and Robert Shaw from the Lorenz equations  The set of ordinary differential equations is
where and are the parameters. This system is invariant under a rotation symmetry around the -axis. For , a chaotic attractor is obtained (Fig. 1).
This system is a companion to the Lorenz system, in the sense that it belongs to the same class of systems. The main departure between the Burke & Shaw system and the Lorenz system is not in their equations but in the way they are organized around the axis . This attractor is characterized by a four branch template (Fig. 2) .
 R. Shaw, Strange attractor, chaotic behavior and information flow, Zeitschrift für Naturforsch A, 36, 80-112, 1981.
 C. Letellier, T. Tsankov, G. Byrne & R. Gilmore, Large-scale structural reorganization of strange attractors, Physical Review E, 72, 026212, 2005.
 C. Letellier, P. Dutertre, J. Reizner & G. Gouesbet, Evolution of multimodal map induced by an equivariant vector field, Journal of Physics A, 29, 5359-5373, 1996.