Chaotic Time-variant Dynamical System

Abstract

The paper deals with the development of scientific backgrounds for the first order infinite-dimensional chaotic systems’ design. We suggest performing this design by replacing real time with some virtual variable, which is defined as a function of time and a system state variable. This virtual variable can be considered as the "new" time and it can be used to define transformation operator, which allows us to describe system dynamics in the "new" time domain by using known differential equations of the chaotic systems. We use the Mackey-Glass system as the initial chaotic system and show two transformations for this system by using different transformation operators. These transformations gave us the possibility to define the high-frequency dynamics for two chaotic systems. These systems can be used in different secured applications.