?
Interactive optimization as a tool for finding the complex periodic solutions in nonlinear dynamics
P. 213–218.
Petrov L. F.
We consider essentially nonlinear dynamical systems with the ability to implement a chaotic behavior and deterministic solutions of various kinds. Among the deterministic solutions, we will highlight a variety of periodic solutions of different periods. This work is devoted to numerical algorithms for constructing and analyzing the stability of periodic solutions of strongly nonlinear dynamical systems.
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 2018 Т. 54 № 10 С. 1299–1312
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 ...
Added: February 12, 2019
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
Dmitriev A., Silchev V., Dmitriev V., , in: Lecture Notes in Electrical EngineeringVol. 489: Applied Physics, System Science and Computers II.: Springer, 2019. P. 237–243.
Mathematical modeling of a stock market functioning is one of the actual and at the same time complex task of the modern theoretical economics. From our point of view, building such mathematical models “ab initio”, by using analogy between the stock market and a certain physical system (in our work, laser), is the most promising ...
Added: October 3, 2018
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
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
Chetverikov V., Journal of Physics: Conference Series 2018 Vol. Volume 955 No. 012025 P. 1–5
The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if ...
Added: February 22, 2018
Ulyanov S., Гурарий М. М., Жаров М. М. et al., В кн.: Международная конференция «Микроэлектроника-2015». Интегральные схемы и микроэлектронные модули: проектирование, производство и применение. Сборник докладов.: М.: Рекламно-издательский центр "ТЕХНОСФЕРА", 2016. С. 449–461.
В работе рассмотрены проблемы моделирования радиотехнических интегральных схем с нанометровыми проектными нормами. Обсуждается новое поколение методов моделирования, рассмотрены основные проблемы построения таких методов и алгоритмов и предложены способы повышения их вычислительной эффективности, приведен ряд полученных результатов. ...
Added: February 19, 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
Dmitriev A., Dmitriev V., Silchev V., WSEAS Transactions on Business and Economics 2017 Vol. 14 No. 33 P. 311–321
This paper proposes a nonlinear dynamical model of stock market. Dynamical variables of the model are the variation of ask and bid price relative to equilibrium values and difference between numbers of market agents in a-state and p-state. A particular market agent being in a-state has maximum amount of valuable information about financial asset and ...
Added: November 24, 2017
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
Belousov F., Труды Института системного программирования РАН 2010 Т. 1 № 56 С. 5–19
В данной работе получены новые достаточные условия для существования единственного решения. Дан итерационный метод нахождения этого периодического решения. Представленный подход может быть применен к достаточно широкому классу обыкновенных дифференциальных уравнений. Возможности такого подхода до конца не изучены и требуют дальнейших исследований. ...
Added: November 24, 2013
Belousov F., Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика 2013 Т. 1 С. 27–37
В работе получены достаточные условия существования единственных решений для одномерных обыкновенных дифференциальных уравнений второго порядка. Цель работы не только в получении таких результатов, но и в демонстрации нового подхода, который может быть применен к более широкому классу дифференциальных уравнений, т.е. могут быть рассмотрены дифференциальные уравнения не только второго, но и более высоких порядков. ...
Added: November 24, 2013
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
Periodic canard trajectories with multiple segments following the unstable part of critical manifold
Krasnosel'skii Alexander M., O'Grady E., Pokrovskii A. et al., Discrete and Continuous Dynamical Systems - Series B 2013 Vol. 18 No. 2 P. 467–482
We consider a scalar fast differential equation which is periodically driven by a slowly varying input. Assuming that the equation depends on scalar parameters, we present simple sufficient conditions for the existence of a periodic canard solution, which, within a period, makes n fast transitions between the stable branch and the unstable branch of the ...
Added: February 11, 2013
Perminov G. I., Финансовые исследования 2012 № 1 (34) С. 110–121
The paper presents results of experimental studies of memory-length financial time series. ...
Added: July 5, 2012