Прикладные задачи нелинейной теории колебаний и волн

Purpose. Purpose of this article is to review recent results (over the past three years) obtained at the Institute of Applied Physics (IAP RAS) relating of applications of the method for constructing optimal empirical models to climatic systems. Methods. This method, developed by the authors of the article, includes the construction of reduced models of the system under study in the form of random dynamical systems.

The purpose of this work is to study the peculiarities of external influence, namely osmotic pressure, on cancer cells. Methods. For this purpose, spatially distributed systems describing the dynamics of a three-dimensional cell lattice, a cell spheroid, and a cell surface have been considered. The studied models are based on the basic principles of hydrodynamics, and their numerical simulation has been performed using a modified Euler method. Results.

Popularisation of the key scientific problems occupied a significant place in D. I. Trubetskov’s work. In memory of this fact, the problem of electromagnetic field affecting biological objects is discussed in a popular manner in this article. This problem has more than a century in it’s history, but still being far from the final solution. Objectives. Analyze the problem of the interaction of electromagnetic fields with biological objects and social structures as complex multielement systems, and assess the possibility of identifying new effects in their behavior.

In experimental studies of the propagation of combustion waves in gaseous media, it was found that, under certain conditions, autowave – spiral or target – patterns appear at the wave front. The purpose of the present study is to propose a mathematical model that can explain this phenomenon based on the known chemical kinetics of hydrogen combustion. Model. The original detailed model was first reduced to four equations that adequately describe the propagation of the combustion wave.

The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator.

Aim. This article presents a review of the non-stationary nonlinear phenomena in backward-wave oscillators (BWO). Methods. Numerical modeling using the nonstationary (time-domain) 1-D, 2-D, and 2-D nonlinear theory of electron beam interaction with a backward electromagnetic wave in the slowly varying amplitude approximation. Results. Main results of nonstationary nonlinear theory of O-type and M-type BWO are presented.