Exponential-Algebraic Maps and Chaos in 3D Autonomous Quadratic Systems

Abstract

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.