Converting a general 3-D autonomous quadratic system to an extended Lorenz-type system

A problem of reducing a general three-dimensional (3-D) autonomousquadratic system to a Lorenz-type system is studied. Firstly, undersome necessary conditions for preserving the basic qualitativeproperties of the Lorenz system, the general 3-D autonomousquadratic system is converted to an extended Lorenz-type system(ELTS) which contains a large class of existing chaotic dynamicalsystems. Secondly, some different canonical forms of the ELTS areobtained with the aid of various nonsingular linear transformationsand normalization techniques. Thirdly, the conjugate systems of theELTS are defined and discussed. Finally, a sufficient condition forthe nonexistence of chaos in such ELTS is derived.