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

Детерминированный хаос

Influence of time delay coupling on the complete synchronization of chaos in chaotic systems with discrete time

In the work the in?uence of time delay of coupling on the complete synchronization of chaos in an interacting systems with discrete time is studied. The system’s behavior is considered in dependence on coupling coe?cient value and delay time value. It is established that coupling with time delay prevents appearance of the complete synchronization of chaos, however it allows the synchronization of periodic and quasi-periodic oscillations.

Diagnostics of phase synchronization by means of coherence

Problems in describing chaotic phase synchronization are connected with ambiguity of de?nition of istantaneous phase as well as with limiting of its applicability by the coherent chaos regime. We demonstrate that this phenomenon can be analysed by means of function of mutual coherence which has not these restrictions.

Stochastic resonance, stochastic synchronization and noise-induced chaos in the duffing oscillator

In present paper the following e?ects in nonlinear oscillator with ?nal dissipation are studied: stochastic resonance, stochastic synchronization and noise-induced chaos. It is shown that stochastic resonance and stochastic synchronization at ?nal dissipation have the same regularities as in the case of overdamped oscillator but are observed at a lower noise level.

Asymmetrical coupling influence on bifurcational mechanizms of antiphase chaotic synchronization destruction

The work is devoted to anti-phase controlled synchronization of chaos in diffusivelly coupled cubic maps. Influence of asymmetry of controlling feed-back coupling on mechanizms of the synchronization loss is considered. A new bifurcational scenarium which includes a sequence of transcritical and saddle-repeller bifurcation has been found. We demonstrate that the same squence of bifurcations can lead to either «bubbling» or «riddling» transitions in dependance of assymetry value.  

Generation of chaotic oscillations in experimental scheme of three cascade-coupled phase systems

Results of experimental investigation of chaotic dynamics of the ensemble of three cascade-coupled phase systems (phase-locked loops) are presented. The possibility of dynamical regimes control by means of coupling parameters changing without changing of inner parameters of elements is demonstrated. Spectral and correlation properties of different chaotic regimes are presented. It is shown, that excitation of chaotically modulated oscillation is possible in wide and homogeneous domains of system parameters.  

Chaotic rf generator based on oscillator with 2.5 degrees of freedom

Chaotic RF generator with bipolar transistor is proposed. Mathematical model of  the generator, oscillator with 2.5 degrees of freedom, is investigated. Generator dynamics is analyzed with Advanced Design System (ADS) software using parameters of a real transistor, properties of the board substrate are taken into account by simulation. ADS simulation results are compared with experimental data.

Chaotic modes of asymmetric circular billiard with beams reflection and refraction

The paper studies the chaotic dynamics in circular asymmetric billiard with beams re?ection and refraction. Phase dynamics is characterized by a variety of dynamics modes, which is connected with the e?ect of traditional chaotization mechanisms as well as with the complicacy of allowable motion laws. In the multisheet symmetric phase space, the circular billiard reconstructions have been analysed its asymmetry degrees changes.

Lorenz attractor in flows of simple shift

In the frame of a model given before for simulation of chaotic dynamics of continuum medium the Lorenz attractor is represented. The simulation is given with the help of the structures that de?ne the geometry of a ?ber bundle associated with 3-dimensional regime of velocity pulsations. Lorenz dynamics appears as time dependence of pulsations along the lines of average ?ow.

Lyapunov exponents in the henon–heiles problem

By the way of combined integrating of the motion and variation equations we calculated the maximal characteristic Lyapunov exponents in the wide limits of energy and time for the Henon–Heiles problem. It follows from the ?tting procedure that the best approximate function is the exponential one with the parameter values, which are di?erent from the earlier obtained parameter values (Benettin et al.).

Sufficient conditions of the lorenz-system homoclinic orbit existence

The property of unstable manifold of the Lorenz-system zero equilibrium is proved. This permited to prove the su?cient condition of homoclinic orbit existence.