This paper shows how the qualitative theory of dynamical systems, that is intensively developed during the last forty years, is currently applied in practice to provide effective wireless ultrawideband communications using chaotic information carrier.
The problem of separation of an observed sum of chaotic signals into the individual components is considered in the presence of noise. A noise threshold is found above which highquality separation is impossible. This effect is shown to be associated with the information content of chaotic signals and a theoretical estimate is given for the threshold. A method for signal separation is proposed, which uses iteration of the chaotic sources equations in reverse time. The method allows to approach the theoretical limit threshold.
In this work, we study information processing applications of complex dynamics and chaos in neural networks. We discuss mathematical models based on piecewise-linear maps which enable us to realize the basic functions of information processing using complex dynamics and chaos. Realizations of these models using recurrent neural-like systems are presented.
An application of complex dynamics and chaos in neural networks to information processing is studied. Mathematical models based on piecewise-linear maps implementing basic functions of information processing via complex dynamics and chaos are discussed. Realizations of these models by neural networks are presented. In contrast to other methods of using neural networks and associative memory to store information, the information is stored in dynamical attractors such as limit cycles, rather than equilibrium points. Retrieval of information corresponds to getting the state into the basin of attraction of the attractor. We show that noise-corrupted information or partial information are sufficient to drive the state into the basin of attraction of the attractor, thus these systems exhibit the property of associative memory.
A method for storing and retrieving information on the stable cycles of one-dimensional maps as proposed in Dmitriev [1991], Dmitriev, Panas & Starkov [1991] is considered. The applicability of this method in storing and retrieving two-dimensional pictures is demonstrated. Possible extensions by compressing information are discussed. An implementation of random access memory using a one-dimensional map is also considered.
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