Динамический хаос

The main moments of the historical development of one of the basic methods of nonlinear systems investigating (the averaging method) are traced. This method is understood as a transition from the so-called exact equation:

Wireless sensor networks that is a fast emerging branch of modern telecommunications are considered in this paper. Particular attention is paid on ultrawideband sensor networks where chaotic radiopulses are used as an information carrier between sensor nodes. Development of such wireless sensor networks became possible after long­term investigations of chaotic oscillations and chaos control.

The possibility of predicting the regular and chaotic dynamics of a discrete map by using artificial neural network is studied. The method of error back­propagation is used for calculation the coefficients of the multilayer network. The predicting properties of the neural network are explored in a wide region of the system parameter for both regular and chaotic behaviors. The dependance of the prediction accuracy from the degree of chaos and from the number of layers of the network is studied.

The digital generators model­based by two­dimensional mappings on toroid, in particular by mapping «Arnold’s Cat», as the built­in sources of entropy working as a part of single­crystal cryptographic systems of generation of random numbers is discussed. The practical scheme of the generator on the binary counters, realised on element base of semiconductor factories is resulted. The comparative characteristic of pumping of entropy generators is discussed. Safety conditions are analyzed.

In the paper we studied properties of conservative singular maps. It was found that under some conditions the intermittency without chaotic phases can be observed in these maps. The alternative mechanism of the intermittency origin in Hamiltonian singular systems was considered. Its general properties were discussed. We studied special properties of phase space structure in these systems. It is shown that Hamiltonian intermittency can be characterized by zero Lyapunov exponents. It gives us the possibility to classify it as pseoudochaos dynamics.

Dynamic chaos – a remarkable milestone development of science of the last centuryhas attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world. What features of the development of science, economic and social conditions led to that long and difficult path of discovery of chaos began precisely at the end of the XIX century and stretched out for decades?