Yuri V. Andreyev

Information processing using dynamical chaos: neural networks implementation

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.

Information processing in 1-D systems with chaos

Mathematical models are proposed, based on one-dimensional piecewise-linear maps, in which complex dynamics, bifurcation phenomena and chaos are used for information processing.

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, CHAOS AND CONTEMPORARY WIRELESS COMMUNICATIONS

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.

Separation of chaotic signal sum into components in the presence of noise

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 high-quality 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 source equations in reverse time. The method allows us to approach the theoretical limit threshold.

Chaotic signal processing: information aspects

Abstract One of the features of chaotic signals that make them different of other types of signals is their special information properties. In this paper, we investigate the effect of these properties on the procedures of chaotic signal processing. On examples of cleaning chaotic signals off noise, chaotic synchronization and separation of chaotic signals we demonstrate the existence of basic limits imposed by information theory on chaotic signal processing, independent of concrete algorithms. Relations of these limits with the Second law, Shannon theorems and Landauer principle are discussed.

Multiplexing chaotic signals in the presence of noise

In this report we discuss the problem of separating the sum of chaotic signals into the individual components with a procedure of backward iteration of the mapping equations describing the chaotic sources. We show that the proposed approach has good stability in respect to additive external noise.

CONDITIONS FOR GLOBAL SYNCHRONIZATION IN LATTICES OF CHAOTIC ELEMENTS WITH LOCAL CONNECTIONS

We investigate the phenomena on the edge of spatially homogeneous chaotic mode and spatiotemporal chaos in a lattice of chaotic 1D maps with local connections. We show that spatially homogeneous chaotic mode cannot exist in a lattice with local connections if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical positive value. We propose a few schemes that make spatial synchronization possible in large lattices. If the idea of only local connections is abandoned, the number of connections necessary for synchronization dramatically decreases to three per node. We also propose a model of a lattice with an external pacemaker, where we find a spatially homogeneous mode synchronous with the pacemaker, as well as different from the pacemaker mode.

Evaluation of the Number of Keys in a Chaotic Cryptographic Method

Data stream coder based on chaotic synchronous response is considered. An estimate of the number of keys available in this scheme is obtained by cascading the basic building block of the system and thus repeating the encoding procedures. Efficiency of the discussed algorithm (in the sense of computational expenses) is evaluated and compared to known cryptographic algorithms. As it is shown, the efficiency increases in the case of smaller number of repetitions and greater number of encoding function parameters.

Separation of chaotic signals using their inherent dynamical nature

Here we describe a method for separating the sum of chaotic signals into the individual components, using the inherent underlying dynamics of the chaotic sources. Capabilities of the method are demonstrated on example of discrete-time systems, one-dimensional logistic maps. We demonstrate that the proposed approach based on backward iteration of the mapping equations describing the chaotic sources has good resistance in respect to additive external noise.

Edge of spatio-temporal chaos in cellular nonlinear networks

We investigate phenomena of the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent /spl lambda/ of the isolated chaotic map is greater than some critical value /spl lambda//sub cr/>0. We proposed a model of a lattice with a pacemaker and found a spatially uniform mode synchronous with the pacemaker, as well as a spatially uniform mode different from the pacemaker mode.