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Two chaotic systems which interact by mutually exchanging a signal built fromtheir delayed internal variables, can synchronize. A third unit may be able torecord and to manipulate the exchanged signal. Can the third unit synchronizeto the common chaotic trajectory, as well? If all parameters of the system arepublic, a proof is given that the recording system can synchronize as well.However, if the two interacting systems use private commutative filters togenerate the exchanged signal, a driven system cannot synchronize. It is shownthat with dynamic private filters the chaotic trajectory even cannot becalculated. Hence two way (interaction) is more than one way (drive). Theimplication of this general result to secret communication with chaossynchronization is discussed.

Chaos Synchronization with Dynamic Filters: Two Way is Better Than One Way