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


нелинейная динамика

Equations with the Fermi–Pasta–Ulam and dislocations nonlinearity

Issue. The class of Fermi–Pasta–Ulam equations and equations describing dislocations are investigated. Being a bright representative of integrable equations, they are of interest both in theoretical constructions and in applied research. Investigation methods. In the present work, a model combining these two equations is considered, and local dynamic properties of solutions are investigated. An important feature of the model is the fact that the infinite set of characteristic numbers of the equation linearized at zero consists of purely imaginary values.

К ПРОБЛЕМЕ СИНХРОНИЗАЦИИ ФИЗИЧЕСКИХ МАЯТНИКОВ

На примере двух компланарных металлических маятников, точки подвеса которых находятся на одном горизонтальном уровне при фиксированном расстоянии b друг от друга, показана принципиальная возможность их синхронизации благодаря учету двух факторов: 1. Эффекту электромагнитного взаимодействия между ними и 2. Учету ЭМ излучения, приводящего к нелинейному затуханию. Получена система нелинейных динамических уравнений движения, и дана численная оценка времени синхронизации.

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.

Models of volume free electron lasers

Several mathematical models of volume free electron lasers are described with the aim of investigation of their nonlinear dynamics. This review includes models of beams of charged particles moving through spatially­periodic systems (photonic crystals). In simulation of volume free electron lasers on the base of photonic crystals made from metallic threads or foils working in the microwave range it was shown the necessity of taking into account dispersion of electromagnetic waves on resonator threads.

Three-­dimensional simulation of virtode with toroidal cavities

The results of preliminary 3D fully electromagnetic simulation of microwave generator with virtual cathode and external feedback loop (virtode) are discussed in this paper. The feedback is realized by the velocity modulation of electron beam in the accelerating gap of electron gun with the electromagnetic signal taken with output cavity placed in the virtual cathode area.

Complex structure and nonlinear behavior of very low frequency of heart rate variability: model of analysis, and practical applications

Researched the structure of Very Low Frequency (VLF) spectrum of heart rate variability (HRV)  and its nonlinear behavior in a relationship with the energy of oscillations, baroreflex and parasympathetic activity at functional tests of low intensity in 100 subjects (seven-test, deep breathing), including active orthostatic test of 32 subjects with orthostatic tachycardia in comparison to the control group of 20 subjects. There were three stages of research. The first  stage: created the method of spectral analysis of separate components of VLF.

From theory of oscillations to nonlinear dynamics

The paper deals with the retrospective consideration of course lectures on theory of oscillations in Nizhny Novgorod university and its evolution during more then 70 years.

The suppression of the excitation of the active medium with a weak external action

This paper presents two new methods of suppressing an impulse in one-dimensional and two-dimensional excitable media using an external influence. In the proposed methods, we used short-impulseinfluence, leading to a change in velocity of the front , which in turn led to the destabilization of  the propagating impulse and transition medium unexcited state. The studies were conducted on the Zykov model that a certain set of parameters is a model of an excitable medium.

About the history of econophysics, nonlinear and evolutionary economics

The paper is devoted to the history of physics and evolutionary biology to economics. This influence began with the birth of economics as a separate field of scientific knowledge and changed  with the development of physics and biology. Strengthening the role of statistical methods in the  physics of the twentieth century, the birth of nonlinear physics, biology, evolution is reflected in the  economy and finance, resulting in the appearance of such area as econophysics, nonlinear and  evolutionary economics.

Using arduino platform in the measurements and the physical experiment

This paper discusses the possibility of a hardware­software platform Arduino, as a relatively simple and flexible tool that could occupy a niche in the research tools. Radiophysical chaotic oscillator with delayed feedback was created on the base of Arduino.

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