(The) proposition of new chaotic systems, and control & synchronization

Abstract

We can easily find a lot of chaos phenomena dotted in our surroundings. Due to the main characteristics of irregularity and unpredictability, chaos phenomena are the target that we have to analyze and control. On the other hand, we can use chaos in various applications such as secure communications, information processing. The mathematical chaotic models have given many disciplines in various fields a good opportunity to figure out the fundamentals and analysis tools of chaos phenomena in nature. And to suppress or eliminate chaos phenomena, and to take advantage of chaos, control schemes are required and have been proposed. A mathematical chaotic model is used to validate the control schemes and to generate chaos behaviors intentionally. In this paper, four new three-dimensional autonomous mathematical chaotic models (usually called chaotic system) are proposed. It is predicted that the proposed chaotic systems contribute additions to the existing chaotic systems with respective characteristics. In addition to it, adopting the robust backstepping control using time delay estimation(BCTDE), the controlling and synchronizing of the Lorenz system and two of the proposed chaotic systems are executed. Numerical simulations show that the BCTDE has fast, accurate, robust performance. The control scheme is also experimentally verified on the physical chaotic system realizing a mathematical chaotic model with analog circuits. The experiment results display good performance and effectiveness against uncertainties.