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

Applied Problems of Nonlinear Oscillation and Wave Theory

Dynamics of the FitzHugh–Nagumo system under external periodic force

In paper on basis of radiophysical experiment analysis of dynamics of the FitzHugh– Nagumo system have been carried out. The dependence of oscillation’s regime in the system from force parameter has been found out. Influence of the form of the external force signal on the system response has been studied.

Modelling of dynamic processes with piecewise linear characteristics

Some problems of modelling of dynamic systems with piecewise linear characteristics are considered. New methods of approximation of the piecewise linear functions, in particular, step functions without disadvantages of the traditional Fourier series expansions are suggested. Some questions of convergence and error estimation of the approximation are explored.

Synchronization of klystron oscillator with delayed feedback in the presence of noise

This work presents experimental results of synchronization of klystron oscillator with delayed feedback in the presence of noise. It was shown, that synchronization effect significantly decreases noise level, leads to amplifying of synchronizing signal and shortening of synchronization wideband. When additive sum of harmonic and noise signal are directed to klystron input, signal-to-noise ratio significantly increases due to synchronization.

Reconstruction of neutral time-delay systems

The methods are proposed for the reconstruction of time-delay systems modeled by neutral delay-differential equations from their time series. The methods are successfully applied to the recovery of generalized Mackey–Glass equation and equations modeling ship rolling and human movement from simulated data.

The modes of genetic structure and population size dynamics in evolution model of two­-aged population

The modes of genetic structure and size dynamics of structured population are investigated in this work. The reproductive potential and survival rate of reproductive part of population in following years of life are determined on genetic level. It has been shown that evolutional increasing of average population fitness is followed by arising of complicated dynamics of population size and of genetic structure.

Controll of multistability by means of bi­phase resonance force

We propose a new method of control of phase multistability in two coupled selfsustained oscillators. The method is based on the «pulling» of phases of oscillations to the target mode under two external harmonic forces, which influence the first and the second sub-systems simultaneosly. Varying the phase shift between the external signals results in control of switching between coexisting oscillating modes. Effectiveness of the method is demonstrated on the example of switching between periodic and chaotic regimes in two Chua’s oscillatotrs.

Synchronization of oscillations in the dynamics of ensembles of surface nephrons

Based on the analysis of experimental data we study the collective dynamics of ensembles from several tens nephrons located on a kidney surface. Using wavelet-analysis, the phenomenon of locking of instantaneous frequencies and phases is studied that is caused by the tubulo-glomerular feedback. It is shown that structural units of the kidney related to distinct nephron trees participate in clusters formation. The entrainment of frequencies and phases of oscillations for large groups of nephrons occurs only for some fragments of experimental data.

Method of empirical modes and wavelet­filtering: application in geophysical problems

Theoretical bases of empirical mode decomposition being one of the new methods of time-frequency analysis of processes with time-varying characteristics are discussed. It is shown that application of this approach together with wavelet-filtering allows one to study in details the structure of multicomponent registered signals recorded in prospecting seismology.

Numerical simulation of nonlinear dynamics in multiple cavity klystron oscillator with delayed feedback by the "partikle-in- cell» method

The 1.5 D code program of numerical simulation of nonlinear nonstationary processes in the klystron-type devices based on the nonstationary L.A. Vainshtein’s theory of cavity excitation and the «particle-in-cell» method for modeling of the electron beam dynamics is developed. The results of numerical simulation of the basic oscillation modes of the fourcavity klystron oscillator with the external delayed feedback are presented.

Numerical simulation of the field emission diode oscillator with photonic crystal resonator

Results of the theoretical analysis of the diode oscillator with a field-emission cathode placed in a photonic crystal resonator are considered. The analysis of conditions of self-excitation in the small signal approximation is carried out. The nonstationary numerical model of the oscillator based on the nonstationary equation of excitation of the resonator and the particle-in-cell method is developed. Numerical simulation of the processes of oscillation build-up is performed.