Applied Problems of Nonlinear Oscillation and Wave Theory

Based on the analysis of experimental data we study the collective dynamics of ensembles from several tens nephrons located on a kidney surface. Using wavelet­analysis, the phenomenon of locking of instantaneous frequencies and phases is studied that is caused by the tubulo­glomerular 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.

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

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.

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. The simulation shows rather high output power and efficiency for reasonable values of cathode current density.

The task is considered of taking into account the multiple time scales of original time series, with these time series being used for Granger causality estimation. It is proposed to use the combination of prediction length and lag, different in value, that could be fruitful for comparatively short times series, e. g. of medical-biological nature. The automated methods are constructed to select lag and prediction length values. The proposed approach is tested on a set of examples – ethalon systems.

The results of operation modes research of the auto-generating system based on a magnetically controlled two-terminal active device with negative differential resistance and N-type current-voltage characteristic are represented. Experimental graphics of oscillatory modes temperature dependencies of the researched dynamic system are given.

Control of phase multistability and synchronization are investigated in two coupled Feigenbaum systems on example of Chua’s generators, coupled through symmetric diffusive link. The control is fulfilled by externel periodic signals, which simultaneously influence the both oscillators with equal amplitudes and frequencies, but with different phases. The behaviour of the system is explored in depandence on amplitude, frequency and phase difference between the signals. Influence of the phase difference on width of the synchronization tongue is considered.

In this paper we make investigation of aperiodic modes Ricker’s model. It’s identified two qualitatively different kinds of aperiodic modes for this model. It’s defined one of the selected types of aperiodic modes. We have called him interval time-periodic mode. For analyze of dynamics of one-dimensional system we used pseudo phase space with a big lag. The maps of the interval of periodic modes are made. We discuss the distribution of interval periodic modes into parameter space of Ricker’s model.

Magnetostatic surface waves propagation in one-dimensional magnonic crystal obtained by etching of array of grooves (56 width, 0.66 deep, period 98 ) in yttrium-iron 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.

The hypothesis about destruction of a coherent mode in system of two mutual couplings microwave oscillators is examine, each of which in a stand­alone mode generates stable unifrequent oscillations. It is experimentally shown, that at strong resonant couplings synchronous oscillations are unstable, therefore the system go over in in a mode of dynamic chaos.