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

Applied Problems of Nonlinear Oscillation and Wave Theory

Influence of first order parametric instability on formation of forbidden gaps in spectra of magnetostatic surface waves in one-dimensional ferrite magnonic crystal

Magnetostatic surface waves propagation in one-dimensional magnonic crystal obtained by etching of array of grooves (56 width, 0.66 deep, period 98 ) in yttriumiron garnet film of 4.1 thickness was investigated at first order (three-magnon) parametric instability. It was shown that forbidden gaps don’t form at region of magnonic crystal where propagation of magnetostatic surface waves is nonlinear because of destroy of phase synchronism of incident and reflected waves. 

Quantum anharmonic oscillator with one-term potential, friction and external force

In the context of the Schrodinger–Langevin–Kostin equation, the quantum anharmonic oscillator with one-term 4-degree potential has been numerically investigated. The generated frequencies of the oscillator are defined by the non-equidistant energy spectra, the number of  discrete frequencies depends on the initial state energy. Due to increasing of initial state energy,  spectra are displaced in the direction of higher frequencies. Influence of friction on transition from  excited state into ground one is also investigated.

About rotational dynamics of a rigid body around non-principal axis passing through the center of mass under dry friction acting

The dynamics is studying for rigid body rotating around fixed axis Oz being central but not principal. Therefore the inertial torques Mx and My arose depending both on mass geometry Jxz, Jyz  and on angular velocity ε and acceleration ε. Dry friction acting on axis’s supports with coefficient δ leads to that the value of ε serves as the reason and result of the motion simultaneously.

Complex structure and nonlinear behavior of very low frequency of heart rate variability: model of analysis, and practical applications

Researched the structure of Very Low Frequency (VLF) spectrum of heart rate variability (HRV)  and its nonlinear behavior in a relationship with the energy of oscillations, baroreflex and parasympathetic activity at functional tests of low intensity in 100 subjects (seven-test, deep breathing), including active orthostatic test of 32 subjects with orthostatic tachycardia in comparison to the control group of 20 subjects. There were three stages of research. The first  stage: created the method of spectral analysis of separate components of VLF.

Synchronization and multi-frequency quasi-periodicity in the dynamics of coupled oscillators

The dynamics of ensembles of oscillators containing a small number of bibitemlits is discussed. The possible types of regimes and pecularities of bifurcations of regular and quasi-periodic attractors are analyzed. By using the method of Lyapunov exponents charts the picture of  embedding of quasi-periodic regimes of different dimension in the parameter space is revealed. Dynamics of ensembles of van der Pol and phase oscillators are compared.

Delay time estimation from time series based on nearest neighbor method

The method is proposed for delay time estimation in time-delay systems from their time series. The method is based on the nearest neighbor method. It can be applied to a wide class of time-delay systems and it is still efficient under very high levels of dynamical and measurement noise.

Blow-­up with complex exponents. Log-­periodic oscillations in the democratic fiber bundle model

The main trend of some blow-up systems is disturbed by log-periodic oscillations infinitely accelerating when approaching the blow-up point. Explanation of such behavior typical e.g. for seismic and economic phenomena could give an insight into the nature of blow-up point rising in this case as the condensation of constant phase points of oscillations. This viewpoint is a particular case of the more general approach that treats not oscillations as a disturbance of the growing trend, but the trend itself as a result of oscillatory process.

Multifractal description of nephrons dynamics

The dynamics of functional units of the kidney in normotensive and hypertensive rats is studied based on the method of multifractal formalism. Rhythmic processes in a nephron’s mathematical model and in experimental data of tubular pressure are analyzed. Changes in singularity spectra for nephronic tubular processes in a hypertension state are illustrated that include an increase of multifractality degree and a decrease of correlations.

Hypermultistability in laser’s models with large delay

We study model of monomode semiconductor laser with optoelectronic feedback, based on balanced equations with delay. We built sets of quasinormal forms in neighboorghood of bifurcation values. The possibility of coexistence of large amount of stable oscillating solutions is shown.

Nonlinear dynamics of helical electron flow in the regime of the virtual cathode forming

We produce the results of computer analysis of complex dynamics of non-relativistic electron beam being placed in crossed electric and magnetic fields, in the regime of a virtual cathod forming in additional braking field. The modeling has been made in the framework of 2D numerical model in the geometry of magnetron-injector gun.

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