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Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems
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 a discrete Shilnikov attractor is described. It is shown that the formation of these attractors leads to the appearance of in-phase bursting oscillations.
Publication based on the results of:
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2026 Vol. 12 No. 1 P. 60–110
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., V. N. Sivkin, Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
N. Belousov, L. Cherepanov, Derkachov S. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
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
Garashchuk I., Kazakov A., Sinelshchikov D., Chaos, Solitons and Fractals 2024 No. 182 Article 114785
We study nonlinear dynamics in a model of three interacting encapsulated gas bubbles in a liquid. The model is a system of three coupled nonlinear oscillators with an external periodic force. Such bubbles have numerous applications, for instance, they are used as contrast agents in ultrasound visualization. Certain types of bubbles oscillations may be beneficial ...
Added: September 8, 2024