1981 The Burke & Shaw system

 The system

The Burke & Shaw system has been derived by Bill Burke and Robert Shaw from the Lorenz equations [1] The set of ordinary differential equations is

where S and V are the parameters. This system is invariant under a rotation symmetry R_z
(pi) around the z-axis. For S=10 and V=4.272), a chaotic attractor is plotted in 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 \(z\) axis [2]. This attractor is characterized by a four branch template as drawn in Fig. 2 [3].