Synchronizing the information content of a chaotic map and flow via symbolic dynamics

In this paper we report an extension to the concept of generalized synchronization for coupling different types of chaotic systems, including maps and flows. This broader viewpoint takes disparate systems to be synchronized if their information content is equivalent. We use symbolic dynamics to quantize the information produced by each system and compare the symbol sequences to establish synchronization. A general architecture is presented for drive-response coupling that detects symbols produced by a chaotic drive oscillator and encodes them in a response system using the methods of chaos control. We include experimental results demonstrating synchronization of information content in an electronic oscillator circuit driven by a logistic map.