Information flow in synchronization

Information theory is used to explore synchronization of unidirectionally coupled chaotic oscillators. A symbolic dynamics is used to identify and tag the emerging information that must be communicated to maintain synchronization. It was recently shown that a minimum channel capacity exceeding the Kolmogorov-Sinai entropy of the drive system is necessary and sufficient to maintain synchronization to any precision. Here, these results are extended to derive fundamental tradeoffs between the precision to which the drive is detected, the quality of synchronization, and the delay or anticipation exhibited by the response. Experimental results using electronic circuits illustrate these tradeoffs.