Robust Control and Synchronization of Chaos
Abstract
In many cases of practical importance, chaotic instabilities limit the performance of devices, such as lasers and electronic oscillators, and hence it is desirable to devise schemes to control the instabilities. During the period of this program, the authors have developed novel algorithms that efficiently control and synchronize chaotic dynamics of high-speed and high-dimensional systems using small perturbations. They have determined the sensitivity of the schemes to noise and slow variation in the system parameters and found that robust controllers and synchronizers can be constructed, but care must be applied in their design. In some situations, dynamical systems can amplify noise by extreme amounts even under conditions when the system is stable. The research has uncovered several fundamental issues related to the control and synchronization of nonlinear systems, which they anticipate will lead to improved performance of devices that are based on nonlinear systems and to the development of chaos-based communication systems. In addition, they have compared experimental observations with detailed theoretical models of the nonlinear dynamical systems to further enhance their understanding of the control and synchronization processes. This paper focuses on the following topics: synchronization of hyperchaotic oscillators, synchronization of periodic oscillators, a new source of ultra-high-speed optical chaos, an array of coupled chaotic electronic circuits, and wide-aperture nonlinear optical resonators. The paper concludes with a list of 10 publications and meeting presentations. (6 figures)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 20, 2003
- Accession Number
- ADA429159
Entities
People
- Daniel J Gauthier
Organizations
- Duke University