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

Deterministic Chaos

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.  

The comparative analysis of synchronization by a harmonious and pulse force by the example of lorentz system

The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.  

Application of continuous wavelet transform to analysis of intermittent behavior

Effective method of signals analysis based on the continuous wavelet transform is proposed in this paper. Application of this method to estimation of mean value both of laminar and turbulent phase durations corresponding to different types of intermittent behavior is considered including analysis of time series produced by living systems. It is shown that the proposed method is stable to noise and fluctuations distorting the initial time series.  

Detection of unstable periodical spatio-temporal states of spatial extended chaotic systems dynamics

The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems dynamics is proposed. The application of this method is illustrated by the consideration of the fluid model of Pierce diode which is one of the base system of plasma physics and of microwave electronics.  

Spectral analysis of oscillations in the system of coupled chaotic self-sustained oscillators

Spectra of oscillations in the system of two coupled self-sustained chaotic oscillators are investigated in present work. The relation between spectra and partial effective phase diffusion coefficients is determined. We follow the evolution of spectra and diffusion coefficients from the asynchronous regime to the regime of synchronous chaos. The analogy between spectral characteristics of coupled chaotic oscillators and noisy coupled periodic oscillators is drawn.  

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

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

Diagnostics of phase synchronization by means of coherence

Problems in describing chaotic phase synchronization are connected with ambiguity of definition 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.

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

In the work the influence 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 coefficient 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.

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 sufficient condition of homoclinic orbit existence. 

Analytical solution of spectral problem for the Perron – Frobenius operator of piece-wise linear chaotic maps

Spectral properties of the linear non-self-adjoint Perron – Frobenius operator of piece-wise linear chaotic maps having regular structure are investigated. Eigenfunctions of the operator are found in the form of Bernoulli and Euler polynomials. Corresponding eigenvalues are presented by negative powers of number of map brunches. The solution is obtained in general form by means of generating functions for eigenfunctions of the operator. Expressions for eigenfunctions and eigenvalues are different for original and inverse maps having even and odd number of branches.