Abstract: In recent years, chaotic behavior of complex nonlinear dynamical networks as a new issue has received a great deal of attention. Since 1963 the Lorenz chaotic oscillator as one of paradigms of chaos has become a focal subject in nonlinear dynamics. Some special topics such as boundedness, convergence, attractive sets, local and global synchronization including well known nonlinear observer and control of chaos have been widely studied for Lorenz type systems. Nonlinear time-varying oscillators and especially chaotic systems can play an important role in many applications including secure and reliable digital communication.
This presentation deals with two important issues that are applicable to chaotic communication systems: synchronization of chaos and controlling chaos. Synchronization of chaos is a naturally occurring phenomenon where one chaotic dynamical system follows dynamical behavior of another chaotic system. This phenomenon can be used in chaotic communication system as a mechanism for information decoding whereas controlling chaos can be used to encode information into the dynamics of the system. Apart from this particular application, the phenomenon of chaotic synchronization is a popular topic of research, in general, and has attracted much attention within the scientific community.
It is not surprising that designing such systems is not as easy as designing linear time-varying systems. Throughout the development of the digital communication, many schemes have been developed to encode and decode information. What is a best scheme that will hide the information so well that it is impossible or almost impossible to intercept the information? This is a question scientist have been working for years. The study of secure communication is the area scientist developed in order to answer the above question. Particularly, secure communication using chaotic system models is a new area where people have put much effort into. The basic idea is that the digital data is somehow embedded into the chaotic signal from a chaotic system, which is in fact a special class of a nonlinear time varying system, and the chaotic signal is transmitted. At the receiver end, knowing the properties of the transmitter system, and only knowing which, we can recover the digital data. So the problems can be designed as: how to design the transmitter and receiver of such a secure communication system; how to embed digital data and transmit the chaotic signal; should the chaotic signal be analog or digital?
Although rich tools for their characterization and analysis are available, we are still in an early stage in terms of their actual design and use. It will also be demonstrated in the presentation that a new state space energy approach, which is closely related to the well known Lyapunov function method can effectively be applied for solving global synchronization and stability problems. This technique has proved to be working for the design of any order chaotic systems, which introduces more flexibility into the design of secure communication systems. Controlling chaos is another potential engineering application. A unique property of controlling chaos is the ability to cause large long-term impact on the dynamics using arbitrarily small perturbations.
In this approach, a study of: various electrical elements needed for the design of nonlinear circuits; the rules for their interconnections; the types of dynamics that will result from such circuits and the types of elements needed for various applications is made. Results, derived from this can be used to design chaotic systems for different applications.


Brief Biography of the Speaker:
Milan Stork received the M.Sc. degree in electrical engineering from the Technical University of Plzen, Czech Republic at the department of Applied electronics in 1974 and Ph.D. degree in automatic control systems at the Czech Technical University in Prague in 1985. In 1997, he became as Associate Professor at the Department of Applied Electronics and Telecommunication, faculty of electrical engineering on University of West Bohemia in Plzen, Czech Republic. He became the full professor in 2007. He is member of editorial board Czech magazine "Physician and Technology" concerning bioengineering. His research interest includes analog/digital linear and nonlinear systems, chaotic systems, control systems, signal processing and biomedical engineering, especially noninvasive tests systems.