Applied Problems of Nonlinear Oscillation and Wave Theory

Simulation of autodyne signal at different feedback level influence on measurement of parameters of vibrating reflector has been performed at different values of optical powerradiation returned in laser resonator. It has been shown that the spectrum of autodyne signal is enrichment when focusing level is increased.

We consider the population dynamics model «predator–prey». Equilibria and limit cycles of system are studied from both deterministic and stochastic points of view. Probabilistic properties of stochastic trajectories are investigated on the base of stochastic sensitivity function technique. The possibilities of stochastic sensitivity function to analyse details and thin features of stochastic attractors are demonstrated.

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N 6 4) are proved to have not less than 2N¡1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2N¡1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

We study synchronization of two coupled nonidentical Bonhoeffer–van der Pol oscillators. Coexistence of two different synchronous regimes is proved. Mechanisms of synchronous regimes origination and destruction are investigated. Fluctuations influence on syncronous regimes is considered. It is found that noise can cause: i) synchronization destruction and beating originations; ii) fluctuations-caused bistability destruction; iii) fluc-tuations-caused intermittency of synchronous regimes without synchronization destruction.

Self-oscillations of wires caused by the vortex separation from the wire surface (so called stall flutter) are considered.

The condition of a bifurcation of a round­trip time of ultrashort pulses (USP) in the Nd­laser with short­time resonant modulation of loss is found out experimentally. This condition is exhibited in the period doubling in the area of a small detunings of the modulation frequency and an intermodal interval. It is revealed, that the pumping level (amplification in the active medium) is a major factor, influencing this effect.

The digital generators model­based by two­dimensional mappings on toroid, in particular by mapping «Arnold’s Cat», as the built­in sources of entropy working as a part of single­crystal cryptographic systems of generation of random numbers is discussed. The practical scheme of the generator on the binary counters, realised on element base of semiconductor factories is resulted. The comparative characteristic of pumping of entropy generators is discussed. Safety conditions are analyzed.

Synchronization between the processes of vegetative regulation of the heart rate and blood pressure in the vessels of microcirculatory channel having in humans a fundamental frequency of about 0.1 Hz is studied. A method for quantitative estimation of the degree of synchronization between these processes is proposed. The method is based on the calculation of a summary percent of phase synchronization of oscillations. A statistical significance of the calculated coefficient of synchronization is analyzed.

The phenomenon of oscillation suppression in ensembles of coupled phase­locked loop systems is discussed. The investigation of this phenomenon was performed for ensembles of three and fifty cascade coupled phase­locked loop systems with first­order filter in control circuits and without it, respectively. The possibilities of oscillation suppression in a part of phase oscillators of ensembles are demonstrated. Domains of the analysed effect existence are determined in the parameter space.

Dynamics and space of сontrol parameters for a nonlinear oscillator under quasi­periodic driving are investigated experimentally by using a nonlinear circuit with p­n junction diode and numerically by using maps and differential equations. The dynamics of the systems under quasiperiodic driving is invariant due to initial driving phases, as a result the plane of the driving amplitudes is symmetrical.