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## Probabilistic issues in the node synchronization problem for large distributed systems

Lobachevskii Journal of Mathematics. 2017. Vol. 38. No. 5. P. 948-953.

We introduce a class of stochastic networks in which synchronization between nodes is modelled by a message passing mechanism with heterogeneous Markovian routing. We present a series of results about probability distribution related to steady states of such models.

Manita A., Journal of Physics: Conference Series 2016 Vol. 681 No. 1 P. 1-6

We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found ...

Added: March 29, 2016

Dmitrichev A., Zakharov D., Nekorkin V., Radiophysics and Quantum Electronics 2017 Vol. 60 No. 6 P. 506-512

We study stability of a synchronous regime in hub clusters of the power networks, which are simulated by ensembles of phase oscillators. An approach allowing one to estimate the regions in the parameter space, which correspond to the global asymptotic stability of this regime, is presented. The method is illustrated by an example of a ...

Added: October 4, 2018

Blank M., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 461 № 2 С. 1-5

We study the functional properties of the concept of interlacing introduced by I.M. Gelfand and show that in the context of collective random walks, this property leads to synchronization. ...

Added: March 20, 2015

Manita A., / Cornell University. Series "Working papers by Cornell University". 2014. No. arXiv:1409.2919.

http://xxx.tau.ac.il/abs/1409.2919 We propose stochastic N -component synchronization models, whose dynamics is described by Levy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components have limits in distribution as t→∞. We give conditions of existence of natural (intrinsic) space scales for large synchronized systemsю. It appears that ...

Added: March 18, 2015

Anatoly Manita, Queueing Systems 2014 Vol. 76 No. 2 P. 149-180

We consider a stochastic model of clock synchronization in a wireless network of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales tN→∞ , N→∞ ...

Added: February 4, 2015

Kuznetsov A., Kuznetsov S., Shchegoleva N. et al., Physica D: Nonlinear Phenomena 2019 Vol. 398 P. 1-12

A problem of synchronization of quasiperiodic oscillations is discussed in application to an example of coupled systems with autonomous quasiperiodic dynamics. Charts of Lyapunov exponents are presented that reveal characteristic domains on the parameter plane such as oscillator death, complete synchronization, phase synchronization of quasiperiodic oscillations, broadband synchronization, broadband quasiperiodicity. Features of each kind of ...

Added: December 2, 2019

Dogonasheva O., Радушев Д. О., Гуткин Б. С. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023

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 is partial synchronization, which may play a pivotal role in elucidating the dynamics of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly denoted as ...

Added: December 12, 2023

Munyaev V., Smirnov L., Kostin V. et al., New Journal of Physics 2020 Vol. 22 Article 023036

We study populations of globally coupled noisy rotators(oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the ...

Added: October 31, 2020

Gong C. C., Toenjes R., Pikovsky A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 2 Article 022206

We propose Möbius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition ...

Added: October 31, 2020

Bolotov M., Smirnov L., Osipov G. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 4 Article 042218

We study how a chimera state in a one-dimensional medium of nonlocally coupled oscillators responds to a homogeneous in space periodic in time external force. On a macroscopic level, where a chimera can be considered as an oscillating object, forcing leads to entrainment of the chimera’s basic frequency inside an Arnold tongue. On a mesoscopic ...

Added: October 31, 2020

Zakharov D., Гуткин Б. С., Krupa M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2018 Vol. 97 No. 6 P. 062211-1-062211-5

We analyzed a generic relaxation oscillator under moderately strong forcing at a frequency much greater that the natural intrinsic frequency of the oscillator. Additionally, the forcing is of the same sign and, thus, has a nonzero average, matching neuroscience applications. We found that, first, the transition to high-frequency synchronous oscillations occurs mostly through periodic solutions ...

Added: October 4, 2018

Пиковский А., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 032210 P. 1-6

Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators— at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and ...

Added: October 31, 2020

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

Volk D., Kleptsyn V., Gorodetski A. et al., Moscow Mathematical Journal 2014 Vol. 14 No. 2 P. 291-308

We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random ...

Added: December 30, 2015

Grishunina S., Теория вероятностей и ее применения 2019 Т. 64 № 3 С. 566-572

This paper is focused on stability conditions of a multi-server queueing system with regenerative input flow where a random number of servers is simultaneously required for each customer and each server's completion time is constant. It turns out that the stability condition depends on the rate of the input flow and not on its structure. ...

Added: August 29, 2019

Пиковский А., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 062210 P. 1-10

The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional ...

Added: October 31, 2020

O. Dogonasheva, Kasatkin D., Boris Gutkin et al., Chaos 2022 Vol. 32 No. 10 Article 101101

Over the past decades, one of the most exciting and fast developed area of modern synchronization theory is the study of chimera states. Such chimera states states are characterized by the coexistence of multiple synchronous and asynchronous domains, despite that the network topology does not at all predict such structures. Moreover, these states are of interest ...

Added: September 16, 2022

Manita A., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012060 P. 1-7

L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from ...

Added: June 21, 2019

Zakharov D., Krupa M., Гуткин Б. С., Communications in Nonlinear Science and Numerical Simulation 2020 Vol. 82 P. 105086

Gamma rhythm (20-100 Hz) plays a key role in numerous cognitive tasks: working memory, sensory processing and in routing of information across neural circuits. In comparison with lower frequency oscillations in the brain, gamma-rhythm associated firing of the individual neurons is sparse and the activity is locally distributed in the cortex. Such “weak” gamma rhythm ...

Added: October 23, 2019

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Borzykh D., ЛЕНАНД, 2021

Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...

Added: February 20, 2021

В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80

Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...

Added: May 3, 2017

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

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