Прикладные задачи нелинейной теории колебаний и волн

The purpose of this work is to develop the reconstruction technique for the neuron-like oscillator equations descibed by a phase-locked system model with delay from scalar time series. Methods. We reconstruct the state vector given a scalar series of only one variable corresponding to the transmembrane potential. The second variable is obtained by numerical differentiation with smoothing by a polynomial. The third variable is obtained by numerical integration using the Simpson method.

Purpose. Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations. Method. Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results. The effect has been found of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems.

The aim of the study is to analytically determine the linear stability of a steady-state operation point for an optical parametric oscillator (OPO) intracavity pumped by a semiconductor disk laser (SDL). Methods. In order to build the analytic approximation to the characteristic equation roots, the method of small-parameter expansion is used. The results of analytic and numerical methods are compared with each other. Results.

Purpose of this work is reduction of differential-difference-model of optic-electronic oscillator to more simple normalized boundary value problems. We study the dynamics of an optoelectronic oscillator with delayed feedback in the vicinity of the zero equilibrium state. The differential-difference-model contains a small parameter with the derivative. It is shown that in a certain neighborhood of the bifurcation point, the number of roots of the characteristic equation that have a real part close to zero increases unlimitedly with decreasing small parameter.

The purpose of this research is to obtain a nonlinear heat conduction equation based on the Stefan–Boltzmann law and energy balance to study the temperature distribution inside the Earth, taking into account usual conductivity and radiant heat conductivity. Resulting equation with a fourth-degree nonlinearity allows to consider the heat transfer between a layer of matter and the environment. Methods to obtain the equation are based on the energy conservation law, taking into account the Kirchhoff’s law and introducing the variation of the blackness coefficient.

The main purpose of this paper is to investigate the dynamics of the power grid model with hub cluster topology based on the Kuramoto equations with inertia. It is essential to study the stability of synchronous grid operation mode and to find conditions of its global stability. The conditions that ensure establishment of the synchronous mode instead of coexisting asynchronous ones are considered. Methods. In this paper we use numerical modelling of different grid operation modes.