ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Strange nonchaotic attractor

An electronic device implementing a strange nonchaotic Hunt–Ott attractor

Topic and aim. The aim of the article is to propose an electronic device representing a non-autonomous dynamical system with a strange nonchaotic attractor insensitive to variation of parameters (with the only limitation that the ratio of the frequencies of the components of the external control driving remains unchanged being equal to a fixed irrational number). Investigated model.

Influence of fluctuations on evolution of three-dimensional torus in nonautonomous system

The transition to chaos through the destruction of three-dimensional torus is studied in a nonautonomous system with quasi-periodic impact as example. Analysis is carried out of the influence both of additive noise and frequency fluctuations impact on the stability of three-dimensional torus. It is shown that under the influence of additive noise and frequency fluctuations impact Lyapunov exponent remains negative. This allows to conclude that in this model three-dimensional torus is structurally stable in contrast to the autonomous system. 

Control parameter space of a nonlinear oscillator under quasiperiodic driving

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.

Strange nonchaotic attractor of Hunt and Ott type in a system with ring geometry

The physical realizable system of ring structure, with a fixed irrational ratio of basic frequencies of external driving (the golden mean) manifests a strange nonchaotic attractor (SNA), similar to the attractor in the abstract map on a torus proposed and analyzed earlier by Hunt and Ott as an example of robust SNA. Simulation of the dynamics is provided basing on the numerical integration of the corresponding non-autonomous system of differential equations with quasi-periodic coefficients.