Communicating with chaos: A physical theory for communication via controlled symbolic dynamics

We present a theory for digital communication based on the fundamental connection between chaos and information theory, and describe an experimental demonstration of the concept. Our primary goal is to describe the salient features of this mechanism for information transfer, not to investigate technological applications. (We do, when appropriate, discuss interesting features of the process and the signals that are not found in classical communication theory, and suggest practical uses.) Our viewpoint is that chaotic systems can be regarded as information sources that naturally produce digital communication signals. By controlling the symbolic dynamics of a chaotic system using small perturbations, we can cause the output waveform to carry a desired sequence of symbols representing a message. Simple chaotic dynamical systems, which include nonlinear oscillators of many types, can produce complex waveforms, and thus provide an "algorithmically efficient" source of complex signals. We focus on theoretical and practical issues concerning this method for global chaos control and its natural connection to communication. We also consider the properties of chaos-generated signals, methods for detection, and the basic theory governing this mechanism for information transfer. (Although we focus on communication, the basic idea of controlling symbolic dynamics can also be used for the control of both periodic and aperiodic orbits, as well as for state-space targeting.) The experiment and numerical examples of control are for systems that can be represented by one-dimensional return maps, but we discuss the extension to higher dimensions, and argue that the extension is possible because of certain basic mathematical facts. (It is likely that the simpler systems with one-dimensional maps will be the first to find a place in technology.) One possible technological realization of our idea would involve the use of a highly nonlinear and efficient analog waveform source operating in its natural chaotic state. Because the analog waveform source is controlled with perturbations that are much smaller than the signal amplitude, all of the complex control and guidance electronics could be microelectronic, even for an extremely high-power source.