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Kuramoto Model with Delay: The Role of the Frequency Distribution
Mathematics. 2023. Vol. 11. No. 10. Article 2325.
Vladimir V. Klinshov, Zlobin A. A.
The Kuramoto model is a classical model used for the describing of synchronization in populations of oscillatory units. In the present paper we study the Kuramoto model with delay with a focus on the distribution of the oscillators’ frequencies. We consider a series of rational distributions which allow us to reduce the population dynamics to a set of several delay differential equations. We use the bifurcation analysis of these equations to study the transition from the asynchronous to synchronous state. We demonstrate that the form of the frequency distribution may play a substantial role in synchronization. In particular, for Lorentzian distribution the delay prevents synchronization, while for other distributions the delay can facilitate synchronization.
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Gusein-Zade S., М.: МЦНМО, 2026.
Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете.
Для студентов математических и физических специальностей. ...
Added: October 12, 2026
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
М.: Юрайт, 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Рудавин Н. В., Ящук В. Ю., Феимов А. А. et al., Журнал технической физики 2026 Т. 96 № 2 С. 341–356
В коммерческих устройствах квантового распределения ключей (КРК) высокая точность синхронизации между генераторами опорных частот передатчика и приемника играет ключевую роль для обеспечения их функционирования. Предложена реализация системы коррекции разницы частот генераторов для устройства КРК. Подробно описаны оптическая схема системы синхронизации, двухступенчатый метод коррекции частот и помехоустойчивый метод автоматического определения момента старта приема и передачи квантовых ...
Added: January 12, 2026
Lubashevsky I., Yashina M., Lubashevskiy V., Synchroinfo Journal 2025 Vol. 11 No. 1 P. 34–40
We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring oscillators when their phases lie within defined interaction sectors. The size of the interaction sector can be seen as a measure of vehicle density within clusters ...
Added: September 23, 2025
Makovkin S., Kozinov E., Ivanchenko M. et al., Scientific Reports 2022 Vol. 12 No. 1 P. 0
Recent in vitro and in vivo experiments demonstrate that astrocytes participate in the maintenance of cortical gamma oscillations and recognition memory. However, the mathematical understanding of the underlying dynamical mechanisms remains largely incomplete. Here we investigate how the interplay of slow modulatory astrocytic signaling with fast synaptic transmission controls coherent oscillations in the network of ...
Added: April 9, 2025
Olesia Dogonasheva, Boris Gutkin, Denis Zakharov, European Physical Journal: Special Topics 2025 Vol. 234 P. 4453–4467
In this paper we consider a pyramidal-interneuron gamma (PING) network consisting of interacting subnetworks of pyramidal cells and interneurons. The main question we have addressed is the dependence of cluster formation processes on the chemical synapse weights and the ionic currents (AHP- and M-current) of the pyramidal neurons that underlie the frequency adaptation and the ...
Added: March 15, 2025
Киселев А. Р., Посненкова О. М., Караваев А. С. et al., Biomedicines 2024 Vol. 12 No. 9 Article 2088
Heart rate variability (HRV) and photoplethysmographic waveform variability (PPGV) are available approaches for assessing the state of cardiovascular autonomic regulation. The goal of our study was to compare the frequency-domain features and low-frequency (LF) synchro nization of the PPGV and HRV with increasing severity of cardiovascular diseases. Methods—Our study included 998 electrocardiogram (ECG) and finger ...
Added: November 25, 2024
Latypov I., Dautova T., Социологические исследования 2024 № 10 С. 15–24
The article offers a review of the sociological concepts of time in order to systematize the available theoretical resources. An analysis of empirical studies of time on the subject of the life course is also given. Social time differs from other types of time that are typical for other disciplines. Time in sociology is understood ...
Added: November 18, 2024
Olesia Dogonasheva, Daniil Radushev, Boris Gutkin et al., Communications in Nonlinear Science and Numerical Simulation 2025 Vol. 140 Article 108321
Methods that distinguish dynamical regimes in networks of active elements make it possible to design the dynamics of models of realistic networks. A particularly salient example of such dynamics is partial synchronization, which may play a pivotal role in emergent behaviors of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly ...
Added: August 31, 2024
Meng-Lin G., Jia-Wei F., Jun-Fan C. et al., Advanced Electronic Materials 2023 Vol. 9 No. 11 Article 2201305
Mode interactions have recently become the focus of intense research in micro/nanoelectromechanical systems (M/NEMS) due to their ability to improve device performance and explore the frontiers of fundamental physics. Understanding and controlling coupling between vibrational modes are critical for the development of advanced M/NEMS devices. This review summarizes the recent advances in studies of coupling ...
Added: November 24, 2023