18 November 1993 Processing information encoded in chaotic sets of dynamic systems
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Abstract
The natural structure of chaotic attracting sets generated by dynamic systems enables the encoding of some information in unstable periodic orbits embedded within the set. Unstable periodic orbits are a hidden invariant of chaotic dynamics, and information encoded in them is, accordingly, hidden. A method for stabilization of unstable periodic orbits of a chaotic attracting set by a weak parametric perturbation of the control parameter has been considered on the example of the Rossler attractor. By this method the hidden information can be extracted from a chaotic set. A hypothetical device of codal-lock-type based on this method is proposed. It is rigorously shown on the example of the logistic map that the action of periodic transformation in the space of parameters corresponding to its chaotic behavior leads to the stabilization of dynamics. As a result, certain functional coupling of two or more logistic maps with chaotic behavior generates stable periodic motion. On the basis of this a possible mechanism of transmitting secure information by chaotic signals is proposed.
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Alexander Y. Loskutov, Valery M. Tereshko, "Processing information encoded in chaotic sets of dynamic systems", Proc. SPIE 2038, Chaos in Communications, (18 November 1993); doi: 10.1117/12.162680; https://doi.org/10.1117/12.162680
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