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## Wild pseudohyperbolic attractor in a four-dimensional Lorenz system

Nonlinearity. 2021. Vol. 34. No. 4. P. 2018-2047.

We present an example of a new strange attractor which, as we show, belongs to a class of wild pseudohyperbolic spiral attractors. We find this attractor in a four-dimensional system of differential equations which can be represented as an extension of the Lorenz system.

Keywords: chaos

Stankevich N., Dvorak A., Astakhov V. et al., Regular and Chaotic Dynamics 2018 Vol. 23 No. 1 P. 120-126

The dynamics of two coupled antiphase driven Toda oscillators is studied. We demonstrate three diﬀerent routes of transition to chaotic dynamics associated with diﬀerent bifurcations of periodic and quasi-periodic regimes. As a result of these, two types of chaotic dynamics with one and two positive Lyapunov exponents are observed. We argue that the results obtained ...

Added: December 2, 2019

Letellier C., Stankevich N., Rössler O., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2022 Vol. 32 No. 2 Article 2230004

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety ...

Added: February 24, 2022

Кузнецов А. П., Stankevich N., Щеголева Н. А., Известия высших учебных заведений. Прикладная нелинейная динамика 2021 Т. 29 № 1 С. 136-159

The purpose of this study is to describe the complete picture of synchronization of two coupled generators of quasi-periodic oscillations, to classify various types of synchronization, to study features of occurrence and destruction of multi-frequency quasi-periodic oscillations. Methods. The object of the research is systems of ordinary differential equations of various dimensions. The work uses the fourth-order Runge–Kutta ...

Added: February 2, 2021

Zhukova N., Chebochko N., Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры 2021 Т. 203 С. 17-38

The aim of this work is to describe the structure of complete Lorentzian foliations $(M, F)$ of codimension two
on $n$-dimensional closed manifolds. It is proved that $(M, F)$ is either Riemannian or has a constant
transversal curvature and its structure is described. For such foliations $(M, F)$, the criterion is obtained,
reducing the chaos problem in $(M, ...

Added: November 17, 2021

Norman G., Stegailov V., Mathematical Models and Computer Simulations 2013 Vol. 5 No. 4 P. 305-333

The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method ...

Added: March 19, 2014

Kazakov A., Ветчанин Е. В., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2016 Vol. 26 No. 4 P. 1650063-1-1650063-13

In this paper, we consider a system governing the motion of two point vortices in a flow excited by an external acoustic forcing. It is known that the system of two vortices is integrable in the absence of acoustic forcing. However, the addition of the acoustic forcing makes the system much more complex, and the ...

Added: June 10, 2016

Shapoval Alexander, Le Mouel J., Shnirman M. G. et al., Astrophysical Journal 2013 Vol. 779 P. 108-116

Sunspot number WN displays quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional l (an “irregularity index”) that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to ...

Added: March 7, 2014

Stankevich N., Shchegoleva N. A., Sataev I. R. et al., Journal of Computational and Nonlinear Dynamics 2020 Vol. 15 No. 11 P. 111001

Using an example a system of two coupled generators of quasiperiodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involve saddle tori occurring at their ...

Added: September 4, 2020

Garashchuk I., Russian Journal of Nonlinear Dynamics 2021 Vol. 17 No. 3 P. 307-320

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes ...

Added: October 19, 2021

Крылосова Д. А., Селезнев Е. П., Stankevich N., Chaos, Solitons and Fractals 2020 Vol. 134 P. 109716

The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of complex chaotic dynamics in the behavior of oscillator. A hierarchy of various periodic and chaotic ...

Added: March 6, 2020

Stankevich N., Kuznetsov A. P., Seleznev E. P., Chaos, Solitons and Fractals 2021 Vol. 147 Article 110998

Appearance of chaotic dynamics as a result of multi-frequency tori destruction is carried out on the example of a model of a multimode generator. Quasiperiodic bifurcations occurring with multi-frequency tori are discussed in the context of the Landau-Hopf scenario. Structure of the parameter space is studied, areas with various chaotic dynamics, including chaos and hyperchaos, ...

Added: May 12, 2021

http://www.shilnikov.unn.ru/en/news.html?id=20, 2020

International Conference "ShilnikovWorkshop-2020" dedicated to the memory of the outstanding Russian mathematician Leonid Pavlovich Shilnikov (1934-2011) will be held on 17-18 December, 2020 at the Lobachevsky State University of Nizhny Novgorod. The topics of the Conference include but not restricted by the following themes of the theory of dynamical systems: bifurcations, strange attractors, conservative and ...

Added: November 1, 2021

Stankevich N., Volkov E., Chaos 2020 Vol. 30 No. 4 P. 043122-1-043122-9

The dynamics of three three-dimensional repressilators globally coupled by a quorum sensing mechanism was numerically studied. This number (three) of coupled repressilators is sufficient to obtain such a set of self-consistent oscillation frequencies of signal molecules in the mean field that results in the appearance of self-organized quasiperiodicity and its complex evolution over wide areas of ...

Added: April 17, 2020

Alexeeva T., Kuznetsov N., Mokaev T., Chaos, Solitons and Fractals 2021 No. 152 Article 111365

Cyclicality and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run.
We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy.
Using of a mid-size ...

Added: September 21, 2021

Li D., Turaev D., Nonlinearity 2020 Vol. 33 P. 971-1015

We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of Cr -diffeomorphisms (r = 3, ... , ∞, ω). This implies the existence of a C2 -open domain in the space of dynamical systems with a certain type of symmetry where systems with heterodimensional cycles ...

Added: October 31, 2020

Stankevich N., Gonchenko A.S., Popova E.S. et al., Chaos, Solitons and Fractals 2023 Vol. 172 Article 113565

We study complex dynamics of the Chialvo model that is the simplest neuron-type model in form of a four-parameter
family of two-dimensional noninvertible maps (endomorphisms). Main elements of bifurcation diagram in the plane of two parameters have been constructed in which regions corresponding to both quasiperiodic and chaotic oscillations are selected. We also indicate special regions corresponding ...

Added: May 21, 2023

Kuznetsov N. V., Mokaev T. N., Alexeeva T. A., Ekaterinburg : Институт математики и механики УрО РАН им. Н.Н. Красовского, 2019

Added: October 30, 2019

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

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

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019