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Новикова С., Потечина И. Петербург – XXI век, 2021.
Shchur L., Antonov D., Burovski E., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2026 P. 1–9
We present a simple model that simulates the possible influence of one society on another. Specifically, two societies evolve deterministically according to the well-known Nowak-May spatial game with the addition of mutual influence through connections that reflect the current states of the societies. This may be related to the influence of a global information resource ...
Added: April 20, 2026
Гаман-Голутвина О.В., Сморгунов Л. В., Полис. Политические исследования 2023 № 1 С. 7–10
The object of consideration in the article is the sources of global turbulence and the understanding of this topic within the framework of modern political science. Among the sources of turbulence are the natural environment and its pulsations, which can destabilize social systems; anthropogenic impact on nature, climate and large ecosystems; unstable demography and powerful ...
Added: December 8, 2025
Shanmugam S., Srinivasan S., Vadivel R. et al., MATHEMATICAL MODELLING AND CONTROL 2025 Vol. 5 No. 1 P. 31–47
In this paper, a recurrent intermittent control (RIC) for the synchronization of fractional-order chaotic neural networks (FOCNNs) is proposed in view of the extended dissipativity-based approach. Successively, standard linear matrix inequalites (LMIs)-based extended dissipative criteria are derived through differential inclusions and inequality mechanisms. Several sufficient conditions are obtained to ensure the synchronization of FOCNNs. Furthermore, ...
Added: July 2, 2025
Tatyana A. Alexeeva, Kuznetsov N., Mokaev T. et al., Chaos, Solitons and Fractals 2025 Vol. 196 Article 116371
Irregular dynamics (especially chaotic) is often undesirable in economics because it presents challenges for predicting and controlling the behavior of economic agents. In this paper, we used an overlapping generations (OLG) model with a control function in the form of government spending as an example, to demonstrate an effective approach to forecasting and regulating chaotic ...
Added: April 20, 2025
Kuptsov P., Ishbulatov Y., Karavaev A. et al., Regular and Chaotic Dynamics 2025 Vol. 30 No. 2 P. 291–305
This study discusses an approach for estimation of the largest Lyapunov exponent for the mathematical model of the cardiovascular system. The accuracy was verified using the confidence intervals approach. The algorithm was used to investigate the effects of noises with different amplitudes and spectral compositions on the dynamics of the model. Three sets of parameters ...
Added: April 8, 2025
Panyushev A., Посненкова О. М., Stankevich N., Proceedings of 2024 8th Scientific School Dynamics of Complex Networks and their Applications (DCNA), Publisher IEEE 2024 P. 181–183
We study different types of multistability in the neuron model with discrete time - the Chialvo map. Multistability of the first type corresponds to the case when resonant and non-resonant invariant curve coexist in phase space. For another parameters of the model we have found coexistence between invariant curve and chaos. We analyze mechanisms of ...
Added: December 1, 2024
Gonchenko S., Гонченко А. С., Морозов К. Е., Radiophysics and Quantum Electronics 2024 Vol. 66 No. 9 P. 693–719
We present a review of some fundamental results in the theory of dynamical systems, which have led to the discovery of dynamical chaos and its three forms, namely, two classical forms, such as conservative chaos and dissipative chaos, as well as the completely new third form, the so-called mixed dynamics in which the sets of ...
Added: November 25, 2024
Manivelan S. V., Srinivasan S., Thamilmaran K. et al., Chaos 2024 Vol. 34 No. 9 Article 091102
In this article, we present evidence of a distinct class of extreme events that occur during the transient chaotic state within network modeling using the Brusselator with a mutually coupled star network. We analyze the phenomenon of transient extreme events in the network by focusing on the lifetimes of chaotic states. These events are identified ...
Added: September 19, 2024
Gordeeva T. O., Marchuk L., Бутенко М. И., Вестник Российского университета дружбы народов. Серия: Психология и педагогика 2024 Т. 21 № 4 С. 967–991
Research activities of postgraduate and undergraduate students are an important component of the educational process and training of qualified specialists who can think and create new knowledge independently, and their choice of research career and, consequently, the scientific, technical and humanitarian progress of our country depends on their productive involvement in it. The results of ...
Added: September 19, 2024
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2024 Vol. 186 Article 115237
We study numerically the dynamics of low–dimensional ensembles of discrete neuron models - Chialvo maps. We are focused on choosing the autonomous map parameters corresponding to the invariant curve. We consider two cases of coupling organization: (i) via a nonlinear function of models; (ii) linear coupling, which is an analog of electrical neuron interaction. For ...
Added: July 10, 2024
Alexeeva T., Кузнецов Н. В., Мокаев Т. Н. et al., Дифференциальные уравнения и процессы управления 2023 № 4 С. 53–66
The accuracy of forecasting the expected values of economic indicators under conditions of irregular dynamics has a key role in taking optimal management decision-making. This current and complex task can be effectively solved using modern methods based on artificial intelligence, the wide introduction of which into the economy is aimed at by the Federal project "Artificial ...
Added: January 7, 2024
Kuznetsov A., Sedova Y., Stankevich N., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2023 Vol. 33 No. 15 Article 2330037
We study the complex dynamics of a discrete analogue of the classical flow dynamical system - R¨ossler oscillator. Minimal ensembles of two and three coupled discrete oscillators with different topologies are considered. As the main research tool we used the method of Lyapunov exponents charts. For coupled systems, the possibility of two-, three- and four-frequency ...
Added: December 13, 2023
Stankevich N., Nonlinear Dynamics 2024 Vol. 112 No. 4 P. 2949–2967
Stabilization by a periodic pulsed force of trajectories running away to infinity in the three-dimensional R ̈ossler system at a threshold of a saddle-node bifurcation, birth of equilibrium states is studied. It is shown that the external pulsed action stabilizes dynamical regimes in a fairly wide range of external signal parameters. Stabilized regimes can be ...
Added: December 12, 2023
Nataliya V. Stankevich, Andrey A. Bobrovskii, Shchegoleva N., Regular and Chaotic Dynamics 2024 Vol. 29 No. 1 P. 120–133
The dynamics of two coupled neuron models - the Hindmarsh-Rose systems, were studied. Their interaction is simulated via chemical coupling that is implemented with sigmoid function. It is shown that complex behavior can occur in the model: quasi-periodic, chaotic and hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos associated with the appearance of ...
Added: November 27, 2023
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
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
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
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
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
Gonchenko S., Kazakov A., Turaev D., 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. ...
Added: October 11, 2021
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
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
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