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

Applied Problems of Nonlinear Oscillation and Wave Theory

Qualitative and numerical analysis of possible synchronous regimes for two inertially coupled van der Pol oscillators

We consider a mechanical system consisting of two controlled masses that are attached to a movable platform via springs. We assume that at the absence of interaction the oscillations of both masses are described by the van der Pol equations. In this case, different modes of synchronous behavior of the masses are observed: in-phase (complete), anti-phase and phase locking. By the methods of qualitative and numerical analysis, the boundaries of the stability domains of these regimes are obtained.

Ring intermittency near the boundary of time scale synchronization

In this paper the intermittent behavior taking place near the boundary of the synchronous time scales of interacted chaotic oscillators being in the synchronous regime is studied. At the regime of time-scale synchronization the system demonstrates synchronous dynamics in a certain range of the time scales whereas the processes on the other time scales remain asynchronous. On the basis of analysis of statistical characteristics of the intermittent behavior, i.e.

Symbolic dynamics in application to cardiac rate study

The analysis of heart rhythms using symbolic dynamics is perfomed. Time intervals corresponding to the predominance of sympathetic or parasym-pathetic tone of the nervous regulation are encoded. During encoding 25 symbols are used, what leads to a wide variety of words in the symbolic strings. The analysis of heart rhythms for patients of all ages, including healthy ones and patients with cardiovascular diseases are produced. These results give characteristic of age-related changes and different pathologies in cardiac rhythms. 

Numerical study of flows past a pair of partially shrouded rotating cylinders

A symmetrical two­dimensional flow past two rotating circular cylinders in a side­by­side arrangement is numerically investigated. Each cylinder is partially covered with an impermeable shroud in such a way that the unshielded moving section faces the incident flow. The effect of flow speed and tangential speed of the cylinder surface on flow topology is investigated for Reynolds numbers from 0 to 100. The formation of stationary eddies – «turrons» – in front of the gap between the cylinders is shown for a wide range of governing parameters.

Treatment of sedov’s solution as series intermediate asymptotics in flow from strong blast

It is offered to consider Sedov’s self-similar solution which earlier was used for exposition only an initial stage of flow from strong blast, in a role of an intermediate asymptotics of matching flow and for any medial, but not so major moment of time. Thus the index of self-similarity should be increased. The upper border of this range is certain from a condition of a constancy of an entropy behind a shock wave.

Phase dynamics of periodically driven quasiperiodic self­-vibrating oscillators

Synchronization phenomena are studied in phase dynamics approximation in the periodically driven system of two coupled oscillators. The cases are discussed when the autonomous oscillators demonstrate phase locking or beats with incommensurate frequencies. Lyapunov charts are presented, the possible regimes of dynamics of the driven system are discussed. Different types of two-dimensional tori are revealed and classified.

Stabilization of chaos in the rossler system by pulsed or harmonic signal

The stabilization of chaos in the Rossler system by external signal is investigated. Different types of external action are considered: both of pulsed and harmonic signal. There are illustrations: charts of dynamical regimes, phase porters, stroboscopic section of Poincare, spectrum of Lyapunov exponents. Comparative analysis of efficiency of stabilization of band chaos and spiral chaos by different signal is carried out. The dependence of synchronization picture on direction of acting pulses is shown.

Self-­similarity at different scale levels in irradiated solid materials

Self-organized structures after ion-beam irradiation in solid materials have been studied using the method of fractal dimension. General computer method of the scale invariance evaluation for exposed dispersive structures is described. It was demonstrated that structures after irradiation can be characterized by the compatibility of scale invariance properties at different scale levels.

Identical chaotic synchronization and bidirectional message transmission in incoherently coupled semiconductor laser diodes

A chaos-based communication scheme allowing simultaneous bidirectional message transmission (Opt. Lett. 32, 403, 2007) is investigated numerically. Incoherent feedback and coupling case is analyzed, which is expected in real long-distance optical communication systems. It is shown that identical synchronization of chaotic laser waveforms and bidirectional message transmission are possible as in the coherent coupling case. However, the chaotic regime at incoherent feedback and coupling is quite different.

Influence of passive elements on the synchronization of oscillatory ensembles

This paper deals with the influence of the passive elements on the synchronization in the ensembles of coupled non-identical Bonhoeffer–van der Pol oscillators. With a help of numerical experiment it was demonstrated that the introduction of passive elements may lead to both increase and decrease of global synchronization threshold in the system. These results were confirmed analytically using piecewise linear approximation of the Bonhoeffer–van der Pol model.