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

Applied Problems of Nonlinear Oscillation and Wave Theory

Optimal data-driven models of forced dynamical systems: General approach and examples from climate

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.

Impact of osmotic pressure on cancer cells in a three-dimensional cellular lattice and cell spheroid

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.

Interaction of electromagnetic radiation with biological objects and social systems

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.

Modeling of wave patterns at the combustion front

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.

Simulation of business and financial cycles: Self-oscillation and synchronization

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.

Nonlinear dynamics of the backward-wave oscillator as the origin of nonstationary microwave electronics

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.

Using a mathematical model of cardiovascular system for preparing surrogate data for testing methods of phase synchronization analysis

The aim of present research is refinement of the parameters and statistical properties of methods for diagnosing
phase synchronization areas based on the dependence of the instantaneous phase difference of oscillations on time.
Methods. Two methods are compared that allow one to identify of synchronization modes based on the dependence of
the instantaneous phase difference of oscillations on time: a method based on an estimate of the phase coherence coefficient

Non-contact atomic force microscope: Modeling and simulation using van der Pol averaging method

Topic and aim. One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. This work aimed at creating the mathematical model of the non-contact atomic force microscope. Models and Methods.

Excitation of phase-controlled oscillator by pulse sequence

The purpose of this work is to study the dynamics of phase-controlled oscillator in excitable mode under rectangular pulse train forcing. The excitable system is a system having a stable equilibrium and a large amplitude periodic pseudo-orbit passing near the equilibrium. Methods. In this paper, the dynamics of the generator under periodic or Poisson rectangular pulse train stimulation is studied by numerical simulation. Different values are proposed to characterize statistics of the oscillator’s responses on different number of stimulating pulses. Results.

Collective classifier learning strategy based upon competition in the coexistence regime

The purpose of this research is to create a new learning strategy for collective classifiers aimed at approximating the Bayesian optimal classification rule. A collective classifier is an ensemble of simple elements, each characterized by a specific response function and free of internal dynamics or variable parameters. Learning is achieved by targeted reshaping the composition of the ensemble (quantities of elements of specific types).

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