Izvestiya of Saratov University.
Physics
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

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Cascade of Invariant Curve Doubling Bifurcations and Quasi-Periodic Hénon Attractor in the Discrete Lorenz-84 Model

Background and Objectives: Chaotic behavior is one of the fundamental properties of nonlinear dynamical systems, including maps. Chaos can be most easily and reliably diagnosed using the largest Lyapunov exponent, which will be positive for the chaotic mode. Unlike flow dynamical systems, the presence of zero Lyapunov exponent in the spectrum is not an obligatory condition for maps. The zero exponent in the spectrum of a map will indicate the possibility of embedding such a map in a flow.

Lorenz Attractor in a System with Delay: an Example of Pseudogyperbolic Chaos

Background and Objectives: The work contributes to a research direction aimed at search for and construction of physically realizable systems, which could fill the mathematical theory of pseudo-hyperbolic dynamics with physical content. Chaotic attractors belonging to this class generate genuine chaos that does not degrade under small variations of parameters and functions in dynamical equations.

Cryptography from the Physicist's Point of View

The results of treating of crypto algorithms such as DES (USA) and GOST 28147-89 (Russia) with the help of nonlinear dynamics methods are presented. Point maps which are generated by the blocks of substitutions (S-blocks) are investigated. The phenomenon of return is demonstrated. The ergodicity of these maps are treated. An estimation of quality of S-block could be made by maps of first return. The results of statistical treating of S-biocks are presented.