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МАТРИЧНАЯ ЛИНЕАРИЗАЦИЯ ФУНКЦИОНАЛЬНО-ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ ТОЧЕЧНОГО ТИПА И ВОПРОСЫ СУЩЕСТВОВАНИЯ И ЕДИНСТВЕННОСТИ ПЕРИОДИЧЕСКИХ РЕШЕНИЙ
Дифференциальные уравнения. 2018. Т. 54. № 10. С. 1299-1312.
Бекларян Л. А.
The work is devoted to periodic solutions of the functional differential equation of point type. In terms of the right-hand side of the original nonlinear functional-differential equation of point type, easily verifiable conditions of existence and uniqueness are formulated, iterative process of constructing such solution is described. In contrast to the scalar linearization, a more complex matrix linearization is used, which allows to extend the class of equations for which the existence and uniqueness of the periodic solution can be established within the framework of this approach.
Belousov F., Бекларян Л. А., Дифференциальные уравнения 2018 Т. 54 № 10 С. 1299-1312
The paper is devoted to periodic solutions of a functional-differential equation of point type. Following the paper \ cite {Beklar_Belous}, in terms of the right-hand side of the original non-linear functional-differential equation of point type, easily verifiable conditions for the existence and uniqueness of the $ \ omega $ -periodic solution are formulated and an ...
Added: June 20, 2018
Beklaryan A., Advances in Systems Science and Applications 2020 Vol. 20 No. 2 P. 56-70
The article discusses construction of traveling wave type solutions for the Frenkel-Kontorova model on the propagation of longitudinal waves. For the first time, based on the existence and uniqueness theorem of traveling wave type solutions, as well as the approximation theorem, a complete family of traveling wave type solutions is constructed in the form of ...
Added: June 30, 2020
Maksimov V. P., Chadov A. L., Известия высших учебных заведений. Математика 2010 № 10 С. 82-86
We consider linear boundary-value problems for systems of functional differential equations when the number of boundary conditions is greater than the dimension of the system. We allow the boundary conditions to be fulfilled approximately. We propose an approach based on theorems whose conditions allow the verification by special reliable computing procedures. ...
Added: November 14, 2012
Belousov F., Бекларян Л. А., Дифференциальные уравнения 2015 Т. 51 № 12 С. 1565-1579
Работа посвящена периодическим решениям функционально-дифференциального уравнения точечного типа. В терминах правой части исходного нелинейного функционально-дифференциального уравнения точечного типа будут сформулированы легко проверяемые условия существования и единственности w-периодического решения, описан итерационный процесс построения такого решения, а также указана скорость сходимости итерационного процесса. ...
Added: April 9, 2015
Vera Ignatenko, Discrete and Continuous Dynamical Systems 2018 Vol. 38 No. 7 P. 3637-3661
A one-parameter family of Mackey-Glass type differential delay equations is considered. The existence of a homoclinic solution for suitable parameter value is proved. As a consequence, one obtains stable periodic solutions for nearby parameter values. An example of a nonlinear functions is given, for which all sufficient conditions of our theoretical results can be verified ...
Added: May 25, 2018
Burov A. A., Косенко И. И., Нелинейная динамика 2017 Т. 13 № 4 С. 519-531
Within the framework of the so-called satellite approximation, configurations of the relative equilibrium are built and their stability is analyzed. In this case the elliptic Keplerian motion of the satellite/the spacecraft tight group mass center is predefined. The attitude motion of the system does not influence its orbital motion. The principal central axes of inertia ...
Added: December 25, 2017
Beklaryan L. A., Beklaryan A., Journal of machine learning and data analysis 2018 Vol. 4 No. 4 P. 220-234
The problem of existence of soliton solutions (solutions of the traveling wave type) for the Korteweg-de Vries equation with a polynomial potential is considered on the basis of the approach within which the presence of a one-to-one correspondence of such solutions with solutions of the induced functional differential equation of pointwise type is demonstrated. On ...
Added: January 11, 2019
Filimonov D., Functional Differential Equations 2004 Vol. 11 No. 3-4 P. 333-339
The system considered in this paper consists of two equations $(k=1,2)$ $\dot x(t)=(-1)^{k-1} (0\le t<\infty),\, k(0)=1,\,x(0)=0,\,x(t)\not\in\{0,1\}(-1\le t<0),$ that change mutually in every instant $t$ for which $x(t-\tau)\in\{0,1\}$, where $\tau={\rm const}>0$ is given. In this paper the behavior of the solutions is characterized for every $\tau\in(\frac{4}{3},\frac{3}{2})$, i. e. in case not covered in \cite{ADM}; as it ...
Added: November 14, 2013
Beklaryan L. A., Beklaryan A., Lobachevskii Journal of Mathematics 2020 Vol. 41 No. 11 P. 2136-2142
Solutions of functional differential equation of pointwise type (FDEPT) are in one-to-one correspondence with the traveling-wave type solutions for the canonically induced infinite-dimensional ordinary differential equation and vice versa. In particular, such infinite-dimensional ordinary differential equations are finite difference analogues of equations of mathematical physics. An important class of traveling-wave type solutions is made up of periodic and bounded ...
Added: September 21, 2020
Бекларян Л. А., Дифференциальные уравнения 2015
Работа посвящена периодическим решениям функционально-дифференциального уравнения точечного типа. В терминах правой части исходного нелинейного функционально-дифференциального уравнения точечного типа будут сформулированы легко проверяемые условия существования и единственности $\omega$-периодического решения, описан итерационный процесс построения такого решения, а также указана скорость сходимости итерационного процесса. ...
Added: February 21, 2015
Beklaryan L. A., Beklaryan A., Computational Mathematics and Mathematical Physics 2020 Vol. 60 No. 8 P. 1249-1260
The importance of functional differential equations of pointwise type is determined by the fact that their solutions are used to construct traveling-wave solutions for induced infinite-dimensional ordinary differential equations, and vice versa. Solutions of such equations exhibit bifurcation. A theorem on branching bifurcation is obtained for the solution to a linear homogeneous functional differential equation of pointwise type. ...
Added: September 21, 2020
Бекларян Л. А., Beklaryan A., Belousov F., Вестник Тамбовского университета. Серия: Естественные и технические науки 2015 Т. 20 № 6 С. 1736-1747
We investigate a problem of the existence of traveling-wave-type solutions for the finite-difference analogue of a nonlinear wave equation. In case of an inhomogeneous medium for vanishing traveling-wave-type solutions a natural extension in the form of quasi-traveling-wave-type solutions is given. ...
Added: December 7, 2015
Chadov A. L., Вестник Пермского научного центра 2013 № 3 С. 13-25
The main results obtained during the project № 10-01-96054 “Mathematical and computer
modeling of ecological and economic state for a region: problems of identification, forecasting,
attainability and control” are described in this paper in a popular form. The aim of the project was to
develop mathematical and software bases for construction of mathematical models complex of
ecological and economic ...
Added: October 25, 2013
Beklaryan A., Beklaryan L., Дифференциальные уравнения 2017 Т. 53 № 2 С. 148-159
The Cauchy problem for the homogeneous linear functional-differential equation of a pointwise type, defined on the line, is considered. In the case of one-dimensional equation we formulated the theorem of existence and uniqueness of solutions with estimating of its order of growth. This research is carried out within the formalism based on group peculiarities of ...
Added: February 12, 2017
Максимов В. П., Chadov A. L., Вестник Пермского университета. Серия: Экономика 2013 № 1(16) С. 6-11
Dynamic models under consideration cover a wide class of models in mathematical Economics and Ecology taking into account some aftereffects and including equations with both continuous and discrete times. Control problems are considered in a general case when the aimes of control are given by a system of linear functionals with an arbitrary number of ...
Added: October 15, 2013
Maksimov V. P., Chadov A. L., Вестник Пермского университета. Серия: Экономика 2012 № 3 С. 12-17
Linear boundary value problems for functional differential systems are considered when the number of boundary conditions is greater than the dimension of the system in the case of approximate fulfilment of boundary conditions. Boundary value problems are connected with studying the problems on the attainability for given indexes of development to the economic system under ...
Added: November 13, 2012
Solvability Problems for a Linear Homogeneous Functional-Differential Equation of the Pointwise Type
Beklaryan A., Beklaryan L. A., Differential Equations 2017 Vol. 53 No. 2 P. 145-156
The Cauchy problem for a linear homogeneous functional-differential equation of the pointwise type defined on a straight line is considered. Theorems on the existence and uniqueness of the solution in the class of functions with a given growth are formulated for the case of the one-dimensional equation. The study is performed using the group peculiarities ...
Added: March 6, 2017
Maksimov V. P., Chadov A. L., Известия высших учебных заведений. Математика 2012 № 9 С. 72-76
We consider control problems for linear systems of functional-differential equations with both continuous and discrete time variables. The goal of controlling the systemunder consideration is prescribed by a finite set of linear functionals. The number of these functionals is independent of the dimension of the system. We describe the subset of controls generated by a ...
Added: November 13, 2012
Условия разрешимости начальной задачи для систем нелинейных функционально-дифференциальных уравнений
Ларионов А. С., Симонов П. М., Sheina M. V., Вестник Тамбовского университета. Серия: Естественные и технические науки 2010 Т. 15 № 2 С. 542-549
Theorems of existence and uniqueness of Cauchy’s problem solution for systems of nonlinear functional and differential equations are proved. During the proof of the theorems the positivity of the Cauchy’s matrix corresponding linear system is used essentially. ...
Added: October 22, 2012
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020