"Information Flow in Synchronization"
Chaos synchronization is a well known mechanism that creates structure in complex dynamical systems, yet many issues remain concerning its limits and robustness. Importantly, chaotic oscillations are characterized by positive entropy; thus, synchronized oscillators must share a common information source. For unidirectional coupling, information generated by the drive must be encoded and transmitted through a coupling channel to a receiver, where it is decoded and used to entrain the response. We use information theory to explore this communication problem. A symbolic description for the oscillator dynamics is used to identify and tag the emerging information that must be communicated to maintain synchronization, and we show there is a minimum channel capacity that is necessary and sufficient to maintain synchronization to any precision. We also explore so-called "achronal" synchronization, in which the response lags or leads the drive by a fixed amount of time. We find fundamental tradeoffs between the precision to which the drive is detected, the quality of synchronization, and the delay or anticipation exhibited by the response. To illustrate these tradeoffs, we present experimental results using electronic circuits.