Encoding information in chemical chaos by controlling symbolic dynamics

In this paper we describe a technique of encoding and then decoding symbol sequences containing information into chaotic oscillations of the Belousov-Zhabotinsky reaction. The encoding technique is based on controlling the chaotic oscillations by applying small parameter perturbations and on learning the grammar of corresponding symbol dynamics produced by the free-running chaotic system. The use of small parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a method for learning the grammar of a symbol dynamics in terms of allowed transitions between the bins defined by the symbol generating partition. The encoding technique can be easily utilized for targeting and stabilization of any unstable periodic orbit.