A system algebraically simpler than the Lorenz system has been proposed by Shimizu & Morioka .
The set of three ordinary differential equations known as the "Shimizu & Morioka" system reads as :
This system has one fixed point, , located at the origin of the phase space and two fixed points located at . For a wide range of parameter values, including those corresponding to a chaotic attractor, is a saddle and are two saddle-foci. This system produces a ``Lorenz-like’’ chaotic attractor with parameter values and (Fig. 1).
Replacing the with 0.191450 changes the attractor for a ``Burke and Shaw-like’’ attractor (Fig. 2).
 T. Shimizu & N. Moroika, On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model, Physics Letters A, 76, 201-204, 1980.