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A physically realizable nonautonomous system of ring structure is considered, which manifests a robust strange nonchaotic attractor (SNA), similar to the attractor in the map on a torus proposed earlier by Hunt and Ott. Numerical simulation of the dynamics for the corresponding non-autonomous set of differential equations with quasi-periodic coefficients is provided. It is demonstrated that in terms of appropriately chosen phase variables the dynamics is consistent with the topology of the mapping of Hunt and Ott on the characteristic period. It has been shown that the occurrence of SNA agrees with the criterion of Pikovsky and Feudel. Also, the computations confirm that the Fourier spectrum in sustained SNA mode is of intermediate class between the continuous and discrete spectra (the singular continuous spectrum). [ABSTRACT FROM AUTHOR]

Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow. [ABSTRACT FROM AUTHOR]

We provide a multiparameter analysis of dynamics in a nonautonomous system of two alternately exciting self-oscillatory elements that are able to demonstrate a uniformly chaotic attractor of Smale-Williams type in the stroboscopic Poincaré map. Parameter space charts of regular and chaotic regimes are presented. Possible scenarios of the onset of hyperbolic chaos are discussed. The numerical studies are supplemented by experimental results obtained for a laboratory electronic device. [ABSTRACT FROM AUTHOR]

We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations. [ABSTRACT FROM AUTHOR]

We study the chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects. [ABSTRACT FROM AUTHOR]

In this paper, nonstationary and chaotic dynamics of a gyrotron with a nonfixed field structure have been studied. We discuss the mechanism of transition to self-modulation and chaotic oscillations and present the plane of parameters with different kinds of regimes in a gyrotron. For chaotic attractors, the set of Lyapunov exponents has been calculated. We have estimated the dimensions of chaotic attractors from the Kaplan-Yorke formula and found it to be anomalously high. The explanation of this fact is based on the presence of a large number of high-Q eigenmodes in the gyrotron resonator operating near a critical frequency of the electrodynamic system. [ABSTRACT FROM AUTHOR]

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting, and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them, previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos. [ABSTRACT FROM AUTHOR]

Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale-Williams solenoid in stroboscopic Poincaré map of two alternately excited non-autonomous van der Pol oscillators. The transition occupies a narrow but finite parameter interval and progresses in such way that periodic orbits constituting a 'skeleton' of the attractor undergo saddle-node bifurcation events involving partner orbits from the attractor and from a non-attracting invariant set, which forms together with its stable manifold a basin boundary of the attractor. [ABSTRACT FROM AUTHOR]

We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1:3. [ABSTRACT FROM AUTHOR]