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

Журнал в журнале

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 four-dimensional map based on well-known 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.

Discrete breathers in scalar dynamical models on the plane square lattice

All symmetry related invariant manifolds, admitting localized vibrations, for dynamical models on plane square lattice were found by group­theoretical methods. Discrete breathers were constructed on these manifolds for the model with homogeneous potentials of interparticle interactions and their stability was studied. Nontrivial breather solutions which are not nonlinear normal modes by Rosenberg have been revealed for the above model despite it admits space­time separation of dynamical variables.

On the problem of computation of the spectrum of spatial lyapunov exponents for the spatially extended beam plasma systems

The behavior of the Pierce diode has been considered from the point of view of the spatial Lyapunov exponents. The method of calculation of the spectrum of the spatial Lyapunov exponents for the electron spatial extended systems has been proposed. The autonomous dynamics of the Pierce diode as well as the behavior of two unidirectionally coupled Pierce diodes when the generalized synchronization is taken place have been considered.

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 single-channel experimental data of prospecting seismology.

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.

Parametric instability of autooscillator coupled with remote load. I. Theory

At the autooscillator with weakly reflected remote load the number of one-frequency states – longitudinal modes – increases with the growth of the reflection coefficient and the length of the delay line. A mode of this kind can be unstable in some parameter regions. There can be two types of perturbations: a) the perturbations resulting in a slow evolution of principal mode amplitude and frequency; b) the perturbations in the form of two satellites which frequencies are symmetric from that of the principal mode.

Chaos in volume free electron lasers

Mathematical model of Volume Free Electron Lasers (VFEL) is described. Some aspects and origins of VFEL chaotic dynamics are examined.

Autooscillating system with compensated dissipation: dynamics of approximated discrete map

The pulse-driven van der Pol oscillator with the external pulse amplitude depending on the system variables is considered. The discrete map for values of the system variables just before the pulse moment was obtained by the slow-varying-amplitude method. Further the parameter space of this map was analyzed, and the existence of the Hamiltonian critical behavior in this system was shown. The remarkable fact is that our system is the system with the dissipation depending not only on the parameter values, but on the variable values too.

Numerical investigation of nonlinear nonstationary process in a chain of coupled gyro-backward-wave oscillators

In this work the nonlinear dynamics in a chain of unidirectionally coupled gyrobackward-wave oscillators is studied. In coupled system, when the control parameters of each distributed system are changed, it is possible to show both a developed chaos dynamics and the regimes of stationary oscillations with one frequency.

Optimal chaos suppression and transition processes in сorrected multiparametrical oscillatory systems

In the work we present a two-stage scheme of optimal correction of the dynamic system’s parameters space aimed at the transformation of the system’s chaotic regime into the regular one through minimal intensity of the perturbation. The offered technique is based on combination of the optimal control theory methods with numerical tests of chaos suppression quality.