показатель Ляпунова.

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.

Dynamics and space of сontrol parameters for a nonlinear oscillator under quasi­periodic driving are investigated experimentally by using a nonlinear circuit with p­n junction diode and numerically by using maps and differential equations. The dynamics of the systems under quasiperiodic driving is invariant due to initial driving phases, as a result the plane of the driving amplitudes is symmetrical.

A simple autonomous three­dimensional system is introduced that demonstrates quasiperiodic self­oscillations and has as attractor a two­dimensional torus. The computing illustrations of quasiperiodic dynamics are presented: phase portraits, Fourie spectrums, graphics of Lyapunov exponents. The existing of Arnold tongues on the parametric plane and transition from quasiperiodic dynamics to chaos through destruction of invariant curve in the Poincare section are shown.

In this paper we investigate modified «Arnold cat» map with dissipative terms, in which a hyperbolic chaos exists for small perturbation magnitudes, and in a certain range a hyperbolic chaotic attractor with Cantor transversal structure takes place, collapsing with a further perturbation amplitude increase.