# структурная устойчивость

## Attractor of smale–williams type in a ring system with periodic frequency modulation

A scheme of circular nonautonomous system is introduced, which is supposed to generate hyperbolic chaos. Its operation is based on doubling of phase on complete cycle of the signal transmission. This is a criterion for the Smale–Williams attractor to exist. The performance is realized due to smooth periodic variation of natural frequency in one of the two oscillatory subsystems, which compose the ring, from reference value to the doubled one.

## Technique and results of numerical test for hyperbolic nature of attractors for reduced models of distributed systems

A test of hyperbolic nature of chaotic attractors, based on an analysis of statistics distribution of angles between stable and unstable subspaces, is applied to reduced finitedimensional models of distributed systems which are the modifications of the Swift–Hohenberg equation and Brusselator model, as well as to the problem of parametric excitation of standing waves by the modulated pump.

## Circular nonautonomous generator of hyperbolic chaos

A scheme of circular system is introduced, which is supposed to generate hyperbolic chaos. Its operation is based on doubling of phase on each complete cycle of the signal transmission through the feedback ring. That is a criterion for the attractor of Smale–Williams type to exist. Mathematically, the model is described by the fourth order nonautonomous system of ordinary differential equations. The equations for slowly varying complex amplitudes are derived, and the Poincar ? e return map is obtained. Numerical simulation data are presented.