NONLINEAR DYNAMICS OF SELF-SYNCHRONIZING SYSTEMS

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Abstract
We investigate the self-synchronization of nonlinear systems. The particular system considered is two-coupled, digital phase-locked loops. It is shown that the overall dynamics is far more complicated than that of a single loop, which is governed by a one-dimensional circle map. In the case of two-coupled loops, we observe that the dynamics is governed by explicit mapping equations only for certain regions of the parameter space. In the regions for which mapping equations can be derived, we find the universality class of the coupled loops. Using such a two loop system as a transmitter of a chaotic signal, it is shown how a third loop can synchronize with this signal. Our results may provide one possible solution to the problem of secure communications.

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