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Об обратимой трехмерной системе, содержащей аттрактор и репеллер Лоренца
Дифференциальные уравнения и процессы управления. 2022. № 2. С. 187–204.
We study the problem on the existence of Lorenz-like attractors and repellers in three-dimensional time-reversible systems, as well as the structure of bifurcation scenarios for their emergence. In this connection, we consider a system that is the flow normal form for reversible bifurcations of a fixed point with the triplet (-1,-1,+1) of multipliers. The bifurcation set itself of the indicated reversible bifurcation should be extremely complex (the normal form contains 7 independent parameters). However, we are mainly interested here in bifurcations leading to the appearance of a symmetric pair “Lorenz attractor – Lorenz repeller”, which, as we show, can be studied within the framework of two-parameter subfamilies. In the paper, two main bifurcation scenarios for the emergence of such a pair are described, and also a quite unusual scenario is outlined for the appearance of Lorenz-like attractor and repeller in the case when the system has only two equilibria. The corresponding phenomenon seems new – for comparison, we note that even the Lorenz system has three equilibria: one of them belongs to the attractor, and the other two reside in its “holes”.
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Karatetskaia E., Kazakov A., Safonov K. et al., Journal of Differential Equations 2025 Vol. 430 Article 113189
We study bifurcations of a symmetric equilibrium state in systems of differential equations invariant with respect to a Z4-symmetry. We prove that if the equilibrium state has a triple zero eigenvalue, then pseudohyperbolic attractors of different types can arise as a result of the bifurcation. The first type is the classical Lorenz attractor and the ...
Added: September 18, 2025
S. V. Gonchenko, A. S. Gonchenko, Partial Differential Equations in Applied Mathematics 2024 Vol. 11 Article 100904
We propose a new class of quadratic three-dimensional maps with the axial symmetry and constant Jacobian that is additional to the well-known class of quadratic three-dimensional Hénon maps. We study dynamical properties and bifurcations in three-parameter families of these axial symmetric maps and show that such maps can have discrete Lorenz attractors, including those of ...
Added: July 7, 2025
Сухарев Д. М., Koryakin V., Kazakov A., Известия высших учебных заведений. Прикладная нелинейная динамика 2024 Т. 32 № 6 С. 816–831
Тема работы — аттракторы лоренцевского типа в многомерных системах. Рассматривается шестимерная
модель, описывающая конвекцию в слое жидкости с учетом примесей в атмосфере и жидкости, а также вращения Земли. Основная цель работы — исследование бифуркаций в соответствующей системе и описание сценариев возникновения хаотических аттракторов разного типа. Результаты. Показано, что в рассматриваемой системе может возникать как классический аттрактор ...
Added: December 10, 2024
Karatetskaia E., Kazakov A., Safonov K. et al., Nonlinearity 2024 Vol. 37 No. 12 Article 125009
We show that bifurcations of periodic orbits with multipliers (−1,i,−i) can lead to the birth of pseudohyperbolic (i.e. robustly chaotic) Lorenz-like attractors of three different types: one is a discrete analogue of the classical Lorenz attractor, and the other two are new. We call them two- and four-winged 'Simó angels'. These three attractors exist in an orientation-reversing, ...
Added: November 8, 2024
Kazakov A., Murillo A., Vieiro A. et al., Regular and Chaotic Dynamics 2024 Vol. 29 No. 1 P. 78–99
We consider a homotopic to the identity family of maps, obtained as a discretization of the Lorenz system, such that the dynamics of the last is recovered as a limit dynamics when the discretization parameter tends to zero. We investigate the structure of the discrete Lorenzlike attractors that the map shows for different values of ...
Added: November 2, 2024
M. Kainov, A. Kazakov, Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 14 P. 3451–3467
In this paper we give some known examples of pseudohyperbolic attractors of systems of differential equations and diffeomorphisms and also describe our numerical method for the verification of strange attractors on pseudohyperbolicity. By means of this method we give numerical evidence of the pseudohyperbolicity of the Lorenz attractor in the Lyubimov–Zaks model, the wild spiral ...
Added: February 8, 2023
Yu. V. Bakhanova, S. V. Gonchenko, Gonchenko A. S. et al., Journal of difference equations and applications 2023 Vol. 29 No. 9-12 P. 1184–1201
We describe scenarios for the emergence of Shilnikov attractors, i.e. strange attractors containing a saddle-focus with two-dimensional unstable manifold, in the case of threedimensional flows and maps. The presented results are illustrated with various specific examples ...
Added: May 30, 2022
Малкин М. И., Safonov K., Chaos 2021 Vol. 31 Article 043107
This paper deals with one-dimensional factor maps for the geometric model of Lorenz-type attractors in the form of two-parameter family of Lorenz maps on the interval 𝐼=[−1,1]I=[−1,1] given by 𝑇𝑐,𝜈(𝑥)=(−1+𝑐⋅|𝑥|𝜈)⋅𝑠𝑖𝑔𝑛(𝑥)Tc,ν(x)=(−1+c⋅|x|ν)⋅sign(x). This is the normal form for splitting the homoclinic loop with additional degeneracy in flows with symmetry that have a saddle equilibrium with a one-dimensional unstable manifold. Due ...
Added: September 21, 2021
Kuryzhov E., Karatetskaia E., Mints D., Russian Journal of Nonlinear Dynamics 2021 Vol. 17 No. 2 P. 165–174
We consider the system of two coupled one-dimensional parabola maps. It is well known that the parabola map is the simplest map that can exhibit chaotic dynamics, chaos in this map appears through an infinite cascade of period-doubling bifurcations. For two coupled parabola maps we focus on studying attractors of two types: those which resemble ...
Added: September 8, 2021
Malkin M., Safonov K., Applied Mathematics and Nonlinear Sciences 2020 Vol. 5 No. 2 P. 293–306
We study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps T_{c,epsilon}(x)=(-1+c|x|^{1-epsilon}) sgn(x). This is the normal form for splitting the homoclinic loop in systems which have a saddle equilibrium with one-dimensional unstable manifold and zero saddle value. Due to L.P. Shilnikov results, such a bifurcation corresponds to ...
Added: October 31, 2020
Kazakov A., Karatetskaia E., Safonov K. et al., Журнал Средневолжского математического общества 2019 Т. 21 № 4
For three-dimensional dynamical systems with continuous time (flows), a classification of strange homoclinic attractors, which goes back to the papers S.V. Gonchenko, D.V. Turaev A.L. Shilnikov and L.P. Shilnikov, is proposed. By homoclinic we mean strange attractors containing a specific saddle equilibrium together with its unstable manifold. Moreover, the type of such an attractor is ...
Added: October 18, 2019
Korotkov A., Kazakov A., Леванова Т. А. et al., Communications in Nonlinear Science and Numerical Simulation 2019 Vol. 71 P. 38–49
We investigated the phenomenological model of ensemble of two FitzHugh–Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model the coupling which is implemented by smooth function that approximates rectangular function and reflects main important properties of biological synaptic coupling. The proposed coupling depends on three ...
Added: October 18, 2019
Kazakov A., Известия высших учебных заведений. Радиофизика 2018 Т. 61 № 8-9 С. 729–738
In this paper, a new scenario of the appearance of mixed dynamics in two-dimensional reversible diffeomorphisms is proposed. The key point of the scenario is a sharp increase of the sizes of both strange attractor and strange repeller which appears due to heteroclinic bifurcations of the invariant manifolds of saddle fixed points belonging to these ...
Added: October 26, 2018
Kazakov A., Гонченко А. С., Гонченко С. В. et al., Известия высших учебных заведений. Радиофизика 2018 Т. 61 № 10 С. 867–882
We study dynamical properties of a Celtic stone moving along the plane. Both one- and two-parameter families of the corresponding nonholonomic models are considered, in which bifurcations are studied that lead to changing types of stable motions of the stone as well as to the onset of chaotic dynamics. It is shown that multistability phenomena ...
Added: October 26, 2018