General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations

Abstract

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.