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

Applied Problems of Nonlinear Oscillation and Wave Theory

Synchronization in coupled self­sustained oscillators with non­-identical parameters

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Andronov–Hopf bifurcation and nonlinear dissipation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Non-identity of parameters of nonlinear dissipation results in specific form of the boundary of the main synchronization tongue, which looks like the mirror letter S.

Autonomous generator of quasiperiodic oscillations

A simple autonomous three-dimensional system is introduced that demonstrates quasiperiodic self-oscillations and has as attractor a two-dimensional torus. The computing illustrations of quasiperiodic dynamics are presented: phase portraits, Fourie spectrums, graphics of Lyapunov exponents. The existing of Arnold tongues on the parametric plane and transition from quasiperiodic dynamics to chaos through destruction of invariant curve in the Poincare section are shown.

Experiments with a source of chaos – a radio­electronic device with square­law phase modulator and interference amplification of quasi­harmonic signal

A modified radio­electronic analog of the nonlinear ring cavity is realized in laboratory. The device represents a special class of oscillations or waves sources. An operation principle of the sources is based on interference amplification of feedback signal by an input signal. A laboratory experiments are performed, the likeness of their results and simulation data is shown. An intermittency, chaos, regular, static modes are detected. A thesis on controlled nonlinearity of dynamical systems is suggested.

Revealing nonlinear couplings between stochastic oscillators from time series

The problem of detection and quantitative characterization of nonlinear directional couplings between stochastic oscillators is considered. Coupling characteristics and a technique for their estimation from time series are suggested. An analytic expression for a statistical significance level of the conclusion about coupling presence is derived that allows a reliable inference from relatively short signals. Performance of the approach is demonstrated in numerical experiments with diverse individual properties of oscillators and different kinds of coupling functions.

New approach to numerical research of the concrete dynamic systems by methods of pattern recognition and statistical modelling

In the present work the new approach to numerical research of the concrete multidimensional and multiparametric dynamic systems is submitted. The offered approach, in part realized and approved, is based on computer calculation of phase trajectories and on use of pattern recognition methods.

Analysis of stochastic work of the composite voltage stabilizer consisting of two buck converters connected as master–slave by fractal measures of deterministic chaos.

Stochastic operation of the parallel–connected buck convertors is considered. For qualitative analysis of the system the bifurcation diagrams are plotted. Quantitative analysis of chaotic regimes was realized by computing of main and special fractal dimensions.

Noise-­induced phase transitions in competition processes in the external fluctuated media

The influence of external additive homogeneous isotropic field of Gauss fluctuations to evolution of competition processes, which described by Lotka–Volterra equations, where taking into account the mobility of weak population individuals and spatial and temporal fluctuations of resource, has been researched. The numerical simulation of considered model was performed.

Conformational B–A transition in the model of DNA molecule with asymmetric double­well interaction potential of nucleotides

In this paper we consider a modified Peyrard–Bishop model with asymmetric doublewell interaction potential of nucleotides and dissipation. It is shown that at the certain value of dissipation coefficient the model solution takes the form of a kink. In terms of DNA molecule it describes the transition between two stable conformational states of DNA molecules – B–A transition.

Chaos in radio device with square­law phase modulator and interference amplification of quasi­harmonic signal: a model and simulation

The attempt is undertaken to define a class of oscillations or waves sources, the operation principle of which is based on interference amplification of feedback signal by an input signal. The precedent here is the optical Ikeda’s system. The radio-electronic analog of a nonlinear ring interferometer and it modification are offered, the block diagrams and mathematical models are constructed. The computer simulation is performed. An intermittency, chaos, regular, static modes are detected.

Nonlinear dynamics of the formation of a spatially inhomogeneous structure in pin diode

The paper presents the results of experimental investigation of stationary distributions of the electric field and the charge carrier concentration in the PIN diode. The investigations have been carried out by use of near­field scanning microwave microscope. Numerical calculations of these values have been performed taking into account the dependence of the mobility and the diffusion coefficient of electrons and holes on the electric field. The alternating maxima and minima form of the field distribution near the contacts and the conductivity has been demonstrated.