New existence conditions of chaos for a wide class of 3D autonomous quadratic dynamical systems are suggested. These conditions are based on the construction and study of properties of algebraic invariants for some 2D quadratic system differential equations.

A method allowing to study the dynamics of 3D systems of quadratic differential equations by the reduction of these systems to the special 2D systems is presented. The mentioned 2D systems are used for the construction of new types of discrete maps generating the chaotic dynamics in some 3D autonomous systems of quadratic differential equations. Strong simplification of all results gives an introduction of the Lambert function. Due to this function some implicit discrete maps become explicit. Examples are given.

For some 3D autonomous quadratic dynamical systems an explicit autonomous exponential-algebraic 1D map, generating chaos in mentioned systems, is designed. Examples of the systems, where chaos is generated by such discrete maps, are given. New results about an existence of chaotic dynamics in the quadratic 3D systems are also derived. Besides, for the Lanford system (it is 3D autonomous quadratic dynamical system) the value of some parameter at which the system shows increased chaotic behavior is indicated. This assertion is based on the construction for the Lanford system of 2D exponential-algebraic discrete map which possesses chaotic properties.

New results about the existence of chaotic dynamics in the quadratic 3D systems are derived. These results are based on the method allowing studying dynamics of 3D system of autonomous quadratic differential equations with the help of reduction of this system to the special 2D quadratic system of differential equations.

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