Generating Lorenz-like and Chen-like attractors from a simple algebraic structure

This paper reports the finding of a very simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. Its algebraic structure is simple with only four linear terms and two quadratic terms. The quadratic terms are different from the Lorenz and the Chen systems. However, by tuning the only parameter, this new family of systems can also generate both Lorenz-like and Chen-like attractors, thus further reveal the close relation between them. © 2014 Science China Press and Springer-Verlag Berlin Heidelberg.