Chaos and information: Using chaotic dynamics for information encoding
Celso Grebogi
Department of Mathematics,
University of Maryland
College Park, MD 20742, USA
It is common for systems to evolve with time in a chaotic way. In practice, however, it is often desired that chaos be avoided or modified for the system to be optimized with respect to some performance criterion. Given a system which behaves chaotically, one approach might be to make some large (and possibly costly) alteration in the system which completely changes its dynamics in such a way as to achieve the desired objectives. Here we assume that this avenue is not available. Thus we address the following question: Given a chaotic system, how can we obtain improved performance and achieve a desired behavior by making only small controlling temporal perturbations in an accessible system parameter. Controlled chaotic systems offer an advantage in flexibility in that any one of a number of different behaviors, chaotic or not, can be stabilized by the small control, and the choice can be switched from one to another depending on the current desired system performance.
I will give many relevant applications to the sciences and engineering including applications to biological systems. In particular, I will show that we can use the close connection between the theory of chaotic systems and information theory in a way that is more than purely formal. I will show that small perturbations can be utilized to cause the symbolic dynamics of a chaotic system to track a prescribed symbol sequence thus allowing us to encode any desired message in the signal from a chaotic oscillator. The natural complexity of chaos thus provides a vehicle for information transmission in the usual sense. Furthermore, I will argure that this method of communication will often have technological advantages. Finally, I will present results of an experiment which demonstrates that chaos can be used to transmit information. In it the symbolic dynamics of a chaotic electrical oscillator is controlled to carry some desired message by using small perturbing current pulses. I will show a movie in which the communication experiment is done in real time.