Time-delay control for stabilization of the Shapovalov mid-size firm model

Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows improvements in forecasting the dynamics of unstable economic processes and offers opportunities for governments, central banks, and other policy makers to modify the behaviour of the economic system to achieve its best performance. One effective method for control of chaos and computation of unstable periodic orbits (UPOs) is the unstable delay feedback control (UDFC) approach, suggested by K. Pyragas. This paper proposes the application of the Pyragas’ method within framework of economic models. We consider this method through the example of the Shapovalov model, by describing the dynamics of a mid-size firm. The results demonstrate that suppressing chaos is capable in the Shapovalov model, using the UDFC method

Microwave generation in synchronized semiconductor superlattices

We study high-frequency generation in a system of electromagnetically coupled semiconductor superlattices fabricated on the same doped substrate. Applying a bias voltage to a single superlattice generates high-frequency current oscillations. We demonstrate that within a certain range of the applied voltage, the current oscillations within the superlattices can be self-synchronized, which leads to a dramatic rise in the generated microwave power. These results, which are in good agreement with our numerical model, open a promising practical route towards the design of high-power miniature microwave generators

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Anisotropic Subdiffractive Solitons

We study solitons in the two-dimensional defocusing nonlinear Schroedinger equation with the spatio-temporal modulation of the external potential. The spatial modulation is due to a square lattice; the resulting macroscopic diffraction is rotationally symmetric in the long-wavelength limit but becomes anisotropic for shorter wavelengths. Anisotropic solitons -- solitons with the square (x,y)-geometry -- are obtained both in the original nonlinear Schroedinger model and in its averaged amplitude equation

Travelling solitons in the parametrically driven nonlinear Schroedinger equation

We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths nonpropogating and moving solitons co-exist while strongly forced solitons can only be stably when moving sufficiently fast.Comment: The paper is available as the JINR preprint E17-2000-147(Dubna, Russia) and the preprint of the Max-Planck Institute for the Complex Systems mpipks/0009011, Dresden, Germany. It was submitted to Physical Review

Time-delay control for stabilization of the Shapovalov mid-size firm model

Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows improvements in forecasting the dynamics of unstable economic processes and offers opportunities for governments, central banks, and other policy makers to modify the behaviour of the economic system to achieve its best performance. One effective method for control of chaos and computation of unstable periodic orbits (UPOs) is the unstable delay feedback control (UDFC) approach, suggested by K. Pyragas. This paper proposes the application of the Pyragas’ method within framework of economic models. We consider this method through the example of the Shapovalov model, by describing the dynamics of a mid-size firm. The results demonstrate that suppressing chaos is capable in the Shapovalov model, using the UDFC method.peerReviewe

Компьютеризация как фактор формирования новой педагогической концепции цифрового образования

The article describes the possibilities of digital devices and resources of the Internet space, allowing to make the educational process accessible, effective, maximally focused on the educational needs of students, Autonomous, individually routed. The article focuses on the technologies that accompany the process of digitalization of education, the principles on which the new pedagogical concept is based, didactic and methodological tools that allow to optimize didactic methods based on the principles of reflection, the development of critical thinking, autonomy, mobility, multilevel.В статье излагаются возможности цифровых устройств и ресурсных средств интернет-пространства, позволяющих сделать образовательный процесс более доступным и эффективным, максимально ориентированным на образовательные потребности обучающихся, автономным, индивидуально маршрутизированным. В статье уделено внимание технологиям, сопровождающим процесс цифровизации образования, принципам, на которых основывается новая педагогическая концепция, дидактическому и методологическому инструментарию, позволяющему оптимизировать дидактические методы на основе принципов рефлексии, развития критического мышления, автономности, мобильности, многоуровневости