# Applied Problems of Nonlinear Oscillation and Wave Theory

## Analytical method of optical wave behavior studying in nonlinear medium with periodically arranged conducting nanofilms

The purpose of this work is to build the analytical model of the behavior of a harmonic wave in a nonlinear optical medium with periodically arranged nanofilms.

## Mathematical model of the photoplethysmogram for testing methods of biological signals analysis

The purpose of this study was to develop a mathematical model of the photoplethysmogram, which can be used to test methods that introduce the instantaneous phases of the modulating signals. The model must reproduce statistical and spectral characteristics of the real photoplethysmogram, and explicitly incorporate the instantaneous phases of the modulating signals, so they can be used as a reference during testing.

## Study of character of modulation instability in cyclotron resonance interaction of an electromagnetic wave with a counterpropagating rectilinear electron beam

In this paper, the interaction of a monochromatic electromagnetic wave with a counterpropagating electron beam moving in an axial magnetic field is considered. The purpose of this study is to investigate the conditions for occurrence of modulation instability (MI) in such a system and to determine at which parameters of the incident wave the MI is absolute or convective.

## Introduction to the statistical theory of differential communication based on chaotic signals

The purpose of this paper is to analyse the statistical characteristics of a Direct Chaotic Differentially Coherent communication scheme based on chaotic radio pulses in a communication channel with additive white Gaussian noise, where the chaotic signal is given by different instantaneous distributions.

Methods. To achieve this goal, numerical modelling of the noise immunity of Direct Chaotic Differentially Coherent communication is conducted and compared with the results of analytical research.

## Analysis of the accuracy of the signal processing algorithm of the differential phase polarimeter

The purpose of this work is to analyze the effect of the polarimeter signal processing algorithm on the results of measurements of the optical rotation angle of the polarization plane to improve the accuracy of measurements in differential polarimetry.

## Spatial and temporal dynamics of the emergence of epidemics in the hybrid SIRS+V model of cellular automata

Purpose of this work is to construct a model of infection spread in the form of a lattice of probabilistic cellular automata, which takes into account the inertial nature of infection transmission between individuals. Identification of the relationship between the spatial and temporal dynamics of the model depending on the probability of migration of individuals.

Methods. The numerical simulation of stochastic dynamics of the lattice of cellular automata by the Monte Carlo method.

## Transfer of passive particles in the velocity field of vortex tripole moving on a plane

Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter.

## Application of joint singularity spectrum to analyze cooperative dynamics of complex systems

Purpose of this work is to generalize the wavelet-transform modulus maxima method to the case of cooperative dynamics of interacting systems and to introduce the joint singularity spectrum into consideration.

The research method is the wavelet-based multifractal formalism, the generalized version of which is used to quantitatively describe the effect of chaotic synchronization in the dynamics of model systems. Models of coupled Rossler systems and paired nephrons are considered.

## Coupled economic oscillations — synchronization dynamical model

Purpose of this work is the research of the dynamical processes and in particular the phenomenon of the synchronization in an ensemble of coupled chaotic economic oscillators.

Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations.

## Mechanisms leading to bursting oscillations in the system of predator–prey communities coupled by migrations

The purpose is to study the periodic regimes of the dynamics for two non-identical predator–prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time.