1999 The "Chen-Ueta" system

In looking for a system that has an algebraic form similar to the one of the Lorenz system but that is not related to it by a diffeormorphism,
Guanrong Chen and Tetsushi Ueta discovered the set of three ordinary differential equations [1]

For appropriate parameter values, this system produces a chaotic attractor (Fig. 1) that is
topologically equivalent to the Lorenz attractor. These parameter values are \(R=22.05\), \(\sigma=35\) and \(b=5\).

For another set of parameter values, that is, for \(R=25.264\), \(\sigma=35\) and \(b=1\), the Chen-Ueta system produces a chaotic attractor (Fig. 2) that is topologically equivalent to the "Burke and Shaw" system. This system does not differ from the other Lorenz-like systems listed in this compilation. It was recently shown that there exists a homothetic transformation
between the Chen-Ueta and the Lorenz systems [2].