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

Applied Problems of Nonlinear Oscillation and Wave Theory

The role of oxygen in Briggs–Rauscher autooscillating reaction

It is description of the way in which chemical environment of Briggs–Rauscher autooscillating reaction affects characteristics of oscillations. It has been ascertained that variations of the iodide complexes concentrations perhaps occurs due to increases of oxygen concentration in media and intermediate’s concentration fluctuation. Influence was investigated one of the basic natural oxidizing agent oxygen and it radical forms on autocooperative mechanisms of Briggs–Rauscher reaction.

Formation of a multi-domain spatial structure in gaas Gunn diode as a nonlinear phenomenon

Experimental studies of stationary distributions of the electric field intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-field microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and diffusion coefficient on the electric field has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and confirmed theoretically.

Bifurcations and transitions to chaos in superlattice coupled to external resonator

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency

Doubling and destruction of the tri-frequencies torus in the nonlinear oscillator under quasi-periodic exitation: experiment

In present paper nonlinear oscillator driving by external force in a form of three harmonic signals with irrational ratios of the frequencies and the map of various dynamical regimes on the parameter plane are presented. The feature of tri-frequencies torus doubling and destruction are investigated.

Autonomous system generating hyperbolic chaos: circuit simulation and experiment

We consider an electronic device, which represents an autonomous dynamical system with hyperbolic attractor of the Smale–Williams type in the Poincare map. Simulation of chaotic dynamics in the software environment Multisim has been undertaken. The generator of hyperbolic chaos is implemented as a laboratory model; its experimental investigation is carried out, and good compliance with the observed dynamics in the numerical and circuit simulation has been demonstrated.

Nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface

Experimental and theoretical study of nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface are conducted. In the work two models are considered for the description of experiments: the analytical model based on the laws of conservation of energy and momentum; the model based on the numerical solution of the nonlinear equation of probe motion. It is shown that the acoustic signal amplitude increases in direct proportion to the oscillations probe amplitude.

Nonlinear systems with fast and slow motions. The change of the probability distribution of fast motions influenced by slow ones

The influence of slow processes (random or regular) on the probability distribution of fast random processes is considered. We show that such influence is universal for all random processes, and in some cases this universality is of the multifractal character. As an example we consider stochastic resonance

On the period-multiplying bifurcation of glacial cycles in the pliocene – pleistocene

In the Pliocene (about five – two million years before present) global climate fluctuated with a period corresponding well 41-thousand-year cycle of changes in the Earth’s axis inclination to the ecliptic plane. Then, this period has disappeared, despite the fact that the 41-thousand-year cycle even slightly increased its scope and, therefore, the response to it would have only strengthened.

Influence of the choice of the model structure for working capacity of nonlinear Granger causality approach

Currently, the method of nonlinear Granger causality is actively used in many applications in medicine, biology, physics, to identify the coupling between objects from the records of their oscillations (time series) using forecasting models. In this paper the impact of choosing the model structure on the method performance is investigated. The possibility of obtaining reliable estimates of coupling is numerically demonstrated, even if the structure of the constructed forecasting model differs from that of the reference system

Effect of rare sampling on estimation of directional couplings from time series

The problem of detection and quantitative estimation of directional couplings (mutual influences) between systems from discrete records of their oscillations (time series) arises in different fields of research. This work shows that results of the traditional «Granger causality» approach depend essentially on a sampling interval (a time step). We have revealed the causes and character of the influence of a sampling interval on numerical values of coupling estimates.

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