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

Applied Problems of Nonlinear Oscillation and Wave Theory

Dynamics of weakly dissipative self-oscillatory system at external pulse influence, which amplitude is depending polynomially on the dynamic variable

Topic and aim. In this work, we study the dynamics of the kicked van der Pol oscillator with the amplitude of kicks depending nonlinearly on the dynamic variable. We choose the expansions of the function cos x in a Taylor series near zero, as functions describing this dependence.

Numerical simulation of oscillations of an electrically charged heterogeneous medium due to inter-component interaction

Aim. The aim of the work is the numerical study of the oscillations of two-phase medium (a mixture of gas and a dispersed phase of solid particles) which caused by electric charge of the dispersed component, and the reciprocal effect of the dynamics of gas and solid particles, as well as the effect of linear size of dispersed particles on the dynamic processes. Methods. With the help of numerical models of electrically charged suspension was modeled in different modes of oscillatory dynamics in a dusty environment. It was assumed that electrically charged are solid particles.

Impact of time delay on the dynamics of optical parametric oscillator with intra-cavity pumping by semiconductor disk laser

Theme. The dynamics of a nonlinear numerical model of a nonlinear optical interaction in the semiconductor disk laser resonator under influence of the time delay is investigated. The conditions of self-excitation, stationary generation modes and their stability are studied. Methods. The analysis of stationary generation stability was performed with DDE-Biftool package. Analysis of higher dimensional regimes was performed using numerical integration, construction of phase portraits, spectra and calculation of Lyapunov exponents. Results.

Frequency repulsion in ensembles of general limit-cycle oscillators synchronized by common noise in the presence of global desynchronizing coupling

Topic. We study the interaction of two fundamentally different synchronization mechanisms: by means of coupling and by means of the driving by a random signal, which is identical for all oscillators – common noise. Special attention is focused on the effect of frequency divergence arising from the competition between these mechanisms. Aim. The aim of the paper is to construct a universal theory describing such an interaction for a general class of smooth limit-cycle oscillators with a global coupling.

Dynamics of equation with two delays modelling the number of population

Issue. The paper investigates the behavior of solutions of a logistic equation with two delays from some neighborhood of the equilibrium state with a large value of the coefficient of linear growth. Such problems arise in modeling the population size taking into account the age structure, as a model of the number of insets, etc. Innovation. It is shown that the critical cases arising in the problem of the stability of an equilibrium state have infinite dimension: an infinitely large number of roots of the characteristic equation tend to the imaginary axis.

SIRS-model with dynamic regulation of the population: Probabilistic cellular automata approach

Aim. Construction a model of infection spread in the form of a lattice of stochastic cellular automata which can demonstrate nontrivial oscillating regimes; investigation of its dynamics and comparison with the mean-field model. Method. Numerical simulation of the square lattice of cellular automata by the Monte Carlo approach, theoretical and numerical study of the structure of the phase space of its mean-field model. Results. A modified SIRS-model of epidemic propagation has been proposed in the form of a lattice of stochastic cellular automata.

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.

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.

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.

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

Experimental studies of stationary distributions of the electric ?eld intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-?eld microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and di?usion coe?cient on the electric ?eld has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and con?rmed theoretically.

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