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


Dynamics of three coupled van der pol oscillators with non-identical controlling parameters

We consider the chain of three dissipatively coupled self-oscillating systems with non-identical controlling parameters. We observe situations, when coupling damps di?erent oscillators. The structure of the frequency mismatch – coupling value parameter plane is investigated with a view to the location of oscillator death area, complete synchronization area, two- and three-frequency quasiperiodic regimes. Features, connected with non-identity in controlling parameters, are considered.

Changes of the parameter plane of driven auto-oscillatory system caused by delayed modulation of the parameter

The driven auto-oscillatory system with the delayed modulation of driving amplitude was investigated. It was shown that synchronous regime destructs in di?erent ways at small and large modulation amplitudes. The changes in the «driving amplitude–driving frequency» plane were revealed.

Electronic circuits manifesting hyperbolic chaos and simulation of their dynamics using software package multisim

We consider several electronic circuits, which are represented dynamical systems with hyperbolic chaotic attractors, such as Smale–Williams and Plykin attractors, and present results of their simulation using the software package NI Multisim 10. The approach developed is useful as an intermediate step of constructing real electronic devices with structurally stable hyperbolic chaos, which may be applicable in systems of secure communication, noise radar, for cryptographic systems, for random number generators.

Effect of noise on generalized synchronization of spatially extended systems described by ginzburg–landau equations

E?ect of noise on generalized synchronization in spatially extended systems described by Ginzburg–Landau equations being in the spatio-temporal chaotic regime is studied. It is shown, that noise does not a?ect the synchronous regime threshold in such systems. The reasons of the revealed particularity have been explained by means of the modi?ed system approach and con?rmed by the results of numerical simulation.

Parametric instability of autooscillator coupled with remote load ii. Numerical simulation

At the autooscillator with small reflection from the remote load the mode stability relative to decay into two side satellites was studied by numerical simulation of characteristic equation. At arbitrary exceed over oscillation threshold the stability regions was founded in the space of system parameters. The results are in a good agree, from the one hand, with theory in the parameter space where characteristic equation can be solved analytically, from the other hand, with the results of numerical simulation of transient processes between modes.

Phenomenon of Lotka–Volterra mathematical model and similar models

Lotka–Volterra mathematical model (often called «predator–prey» model) is applicable for different processes description in biology, ecology, medicine, in sociology investigations, in history, radiophysics, ets. Variants of this model is considered methodologicaly in this review.

About approximate analytical solutions of lotka–volterra equations

The possibility of analytical decision of Lotka–Volterra equation is demonstrated for «predator–prey» model, and for comlicated models.

Time­frequency analysis of nonstationary processes: concepts of wavelets and empirical modes

A comparation of wavelets and empirical modes concepts is performed that represent the most perspective tools to study the structure of nonstationary multimode processes. Their advantages over the classical methods for time series analysis and restrictions of both approaches are discussed that needs to be known for correct interpretation of the obtained results. New possibilities in the study of signals structure at the presence of noise are illuctrated for digital single­channel experimental data of prospecting seismology.

Modeling of cardiac activity on the basis of maps: ensembles of coupled elements

The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio­temporal processes in the myocardium. Particular, the dynamics of two coupled maps is explored as well as modeling the interaction of pacemaker (oscillatory) cell and myocyte (excitable cell), and the interation of two pacemakers.

Modeling of cardiac activity on the basis of maps: dynamics of single element

New computationally efficient model of cardiac activity is introduced. The model is a four­dimensional map based on well­known Luo–Rudy model. Capabilities of the model in replication of the basic cardiac cells’ properties are shown. Analysis of relationship between changes in individual parameters of the model and biophysical processes in real cardiac cells has been made. The model can reproduce two basic activity modes such as excitable and oscillatory regimes. Bifurcation mechanisms of transitions of between these regimes are investigated using phase space analysis.