Chaos synchronization with dynamic filters: Two-way is better than one-wayI. Kanter1, E. Kopelowitz1, J. Kestler2 and W. Kinzel2
1 Department of Physics, Bar-Ilan University - Ramat-Gan, 52900 Israel
2 Institute for Theoretical Physics, University of Würzburg - Am Hubland, 97074 Würzburg, Germany, EU
received 6 February 2008; accepted in final form 15 July 2008; published September 2008
published online 21 August 2008
Two chaotic systems which interact by mutually exchanging a signal built from their delayed internal variables, can synchronize. A third unit may be able to record and to manipulate the exchanged signal. Can the third unit synchronize to the common chaotic trajectory, as well? If all parameters of the system are public, a proof is given that the recording system can synchronize as well. However, if the two interacting systems use private commutative filters to generate the exchanged signal, a driven system cannot synchronize. It is shown that with dynamic private filters the chaotic trajectory even cannot be calculated. Hence two-way (interaction) is better than one-way (drive). The implication of this general result to secret communication with chaos synchronization is discussed.
05.45.Vx - Communication using chaos.
05.45.Xt - Synchronization; coupled oscillators.
05.45.-a - Nonlinear dynamics and chaos.
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