Academic literature on the topic 'Modèle de Kuramoto'
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Journal articles on the topic "Modèle de Kuramoto"
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Buzanello, Guilhermo L., Ana Elisa D. Barioni, and Marcus A. M. de Aguiar. "Matrix coupling and generalized frustration in Kuramoto oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (September 2022): 093130. http://dx.doi.org/10.1063/5.0108672.
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The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a frustrated version that resulted in dynamic behavior of the order parameter, even when the average natural frequency of the oscillators is zero. Here, we consider a generalization of the frustrated KS model that exhibits new transitions to synchronization. The model is identical in form to the original Kuramoto model but written in terms of unit vectors and with the coupling constant replaced by a coupling matrix. The matrix breaks the rotational symmetry and forces the order parameter to point in the direction of the eigenvector with the highest eigenvalue, when the eigenvalues are real. For complex eigenvalues, the module of order parameter oscillates while it rotates around the unit circle, creating active states. We derive the complete phase diagram for the Lorentzian distribution of frequencies using the Ott–Antonsen ansatz. We also show that changing the average value of the natural frequencies leads to further phase transitions where the module of the order parameter goes from oscillatory to static.
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Lysenko, I. O. "Analysis of the Formation of Stationary Patterns at the Ion Sputtering within the Anisotropic Kuramoto–Sivashinsky Model." Ukrainian Journal of Physics 61, no. 7 (July 2016): 588–96. http://dx.doi.org/10.15407/ujpe61.07.0588.
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Ódor, Géza, István Papp, Shengfeng Deng, and Jeffrey Kelling. "Synchronization transitions on connectome graphs with external force." Frontiers in Physics 11 (March 9, 2023). http://dx.doi.org/10.3389/fphy.2023.1150246.
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We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of external excitation. By numerical solution we determine the crackling noise durations with and without thermal noise and show extended non-universal scaling tails characterized by the exponent 2 < τt < 2.8, in contrast with the Hopf transition of the Kuramoto model, without the force τt = 3.1(1). Comparing the phase and frequency order parameters we find different synchronization transition points and fluctuation peaks as in case of the Kuramoto model, related to a crossover at Widom lines. Using the local order parameter values we also determine the Hurst (phase) and β (frequency) exponents and compare them with recent experimental results obtained by fMRI. We show that these exponents, characterizing the auto-correlations are smaller in the excited system than in the resting state and exhibit module dependence.
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Peng, Hao, Wei Wang, Pei Chen, and Rui Liu. "DEFM: Delay-embedding-based forecast machine for time series forecasting by spatiotemporal information transformation." Chaos: An Interdisciplinary Journal of Nonlinear Science 34, no. 4 (April 1, 2024). http://dx.doi.org/10.1063/5.0181791.
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Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens’ delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto–Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.
Dissertations / Theses on the topic "Modèle de Kuramoto"
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Phung, Thanh Tam. "Vers un modèle particulaire de l'équation de Kuramoto-Sivashinsky." Phd thesis, Université d'Orléans, 2012. http://tel.archives-ouvertes.fr/tel-00789952.
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Dans cette thèse, on étudie des systèmes de particules en interaction dont le comportement est lié à certaines équations aux dérivées partielles lorsque le nombre de particules tend vers l'infini. L'équation de Kuramoto-Sivashinsky modélise par exemple la propagation de certains fronts de flamme, la topographie de la surface d'une couche mince en cours de croissance, et fait apparaître des structures macroscopiques. Un modèle de particules en interaction par un couplage harmonique des vitesses, attractif aux premières vitesses voisines, répulsive aux secondes voisines, associée à des collisions élastiques, produit des profils de vitesses analogues aux fronts de flamme. On observe également la création et l'annihilation d'agrégats de particules. Un autre modèle, où les particules fusionnent lors des collisions en préservant masse et quantité de mouvement, et avec uniquement attraction au plus proche voisin, permet de retrouver un modèle de type gaz sans pression avec viscosité. Ces modèles sont étudiés théoriquement, en particulier les facteurs de mise à l'échelle des forces d'interaction sont précisés pour obtenir les équations correctes dans la limite du grand nombre de particules. Des simulations numériques confirment la validité et la pertinence des modèles.
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Koeth, Felix. "Enquêtes sur les propriétés spectrales dans les systèmes électriques." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAT082.
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Cette thèse porte sur les propriétés fondamentales d'un modèle simplifié de système d'alimentation dynamique. Ces modèles permettent d'étudier l'influence des propriétés géométriques du réseau décrivant le système électrique. Ces modèles et certaines propriétés importantes des modèles sont présentés au chapitre 1. L'un des principaux défis de la recherche sur les systèmes électriques est la complexité du système. Nous voulons utiliser la théorie du graphique spectral pour décomposer le système en différents modes, qui peuvent être étudiés individuellement. Le deuxième chapitre présente le contexte mathématique de la théorie des graphes spectraux et les applications aux systèmes d'alimentation. Un exemple simple d'application de la théorie des graphes spectraux à la recherche sur les systèmes d'alimentation est donné au chapitre 3, où l'on étudie le système d'alimentation statique. Nous pouvons voir que les valeurs propres et les vecteurs propres de la matrice d'admission nodale du système électrique peuvent être utilisés pour calculer les phases et les flux dans un système statique. Les propriétés dynamiques sont ensuite étudiées plus en profondeur dans le chapitre suivant. Ici, un problème de valeur propre quadratique doit être utilisé pour étudier le système. Nous présentons les propriétés fondamentales du problème de la valeur propre quadratique et son application à la recherche sur les systèmes d'alimentation. Une étude approfondie des propriétés spectrales d'un système de puissance dynamique utilisant le problème des valeurs propres quadratiques est ensuite réalisée. Nous observons des interactions à courte et longue portée dans le système et constatons que les interactions à courte portée sont plus sensibles aux paramètres de la machine et sont importantes pour la stabilité du système électrique, car elles sont liées aux modes locaux de la centrale. L'émergence de ce comportement localisé est étudiée au chapitre 5. Nous dérivons deux limites de vecteurs propres qui peuvent être utilisées pour prédire et décrire la localisation dans un réseau. Ces limites sont ensuite appliquées à des exemples simples de graphiques et à un cas de test de système électrique, pour montrer comment ils peuvent prédire, expliquer et décrire avec succès la localisationThis thesis investigates the fundamental properties of a simplified dynamical power system model. These models can be used to study the influence of the geometrical properties of the network describing the power system. These models and some important properties of the models are presented in chapter 1. One of the main challenges in power system research is the complexity of the system. We want to use spectral graph theory to decompose the system into different modes, which can be studied individually. The second chapter introduces the mathematical background of spectral graph theory and the applications to power systems. A simple example for the application of spectral graph theory in power system research is given in chapter 3, where the static power flow system is investigated. We can see that the eigenvalues and eigenvectors of the nodal admittance matrix of the power system can be used to calculate the phases and flows in a static system. The dynamical properties are then deeper investigated in the next chapter. Here, a quadratic eigenvalue problem has to be used to investigate the system. We introduce the fundamental properties of the quadratic eigenvalue problem and the application to power system research. An extensive investigation of the spectral properties of a dynamical power system using the quadratic eigenvalue problem is then performed. We observe short and long range interactions in the system and see that the short range interactions are more sensitive to the machine parameters and are important for the stability of the power system, as they are related to local plant modes. The emergence of this localised behaviour is investigated in chapter 5. We derive two eigenvector bounds which can be used to predict and describe localisation in a network. These bounds are then applied to simple example graphs and a power system test case, to show how they can successfully predict, explain and describe localisation
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Oukil, Walid. "Systèmes couplés et morphogénèse auto-organisation de systèmes biologiques." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0459/document.
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On s’intéresse dans cette thèse à des systèmes couplés de type champ moyen en étudiant l’existence de l’état de synchronisation qui se caractérise par une distance uniformément bornée dans le temps entre chaque paire de composantes d’une solution. L’étude se base sur une méthode perturbative. Néanmoins les résultats obtenus ne sont pas évidents dans le cas non-perturbé. En outre dans le cas où le système couplé est périodique et grâce au Théorème du point fixe on montre l’existence d’une solution périodique sur le tore. L’étude de stabilité et de stabilité exponentielle est établie dans le cas linéaire et appliquée à ce type de systèmes couplésWe study in this thesis a class of a perturbed interconnected mean-field system, also known as a coupled systems. Under some assumptions we prove the existence of an invariant open set by the flow of the perturbed system ; in other word, we prove that the distance between the components of an orbit is uniformly bounded, this property is also called synchronization. We use the perturbation method to obtain the result. However the result is not trivial for the not perturbed system. We use the fixed point theorem to prove the existence of a periodic orbit in the torus. We study in addition the stability and the exponential stability of such systems by studying the stability of a linear systems
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El, Ati Ali. "Synchronization analysis of complex networks of nonlinear oscillators." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112362/document.
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Cette thèse porte sur l'analyse de la synchronisation des grands réseaux d'oscillateurs non linéaires et hétérogènes à l'aide d'outils et de méthodes issues de la théorie du contrôle. Nous considérons deux modèles de réseaux; à savoir, le modèle de Kuramoto qui considère seulement les coordonnées de phase des oscillateurs et des réseaux composés d'oscillateurs non linéaires de Stuart-Landau connectés par un couplage linéaire.Pour le modèle de Kuramoto nous construisons un système linéaire qui conserve les informations sur les fréquences naturelles et sur les gains d'interconnexion du modèle original de Kuramoto. Nous montrons en suite que l'existence de solutions à verrouillage de phase du modèle de Kuramoto est équivalente à l'existence d'un tel système linéaire avec certaines propriétés. Ce système est utilisé pour formuler les conditions d'existence de solutions à verrouillage de phase et de leur stabilité pour des structures particulières de l'interconnexion. Ensuite, cette analyse s'est étendue au cas où des interactions attractives et répulsives sont présentes dans le réseau. Nous considérons cette situation lorsque les gains d'interconnexion peuvent être à la fois positif et négatif. Dans le cadre de réseaux d'oscillateurs de Stuart-Landau, nous présentons une nouvelle transformation de coordonnées du réseau qui permet de réécrire le modèle du réseau en deux parties: une décrivant le comportement de l'oscillateur « moyenne » du réseau et la seconde partie présentant les dynamiques des erreurs de synchronisation par rapport à cet oscillateur « moyenne ». Cette transformation nous permet de caractériser les propriétés du réseau en termes de la stabilité des erreurs de synchronisation et du cycle limite de l'oscillateur « moyenne ». Pour ce faire, nous reformulons ce problème en un problème de stabilité de deux ensembles compacts et nous utilisons des outils issus de la stabilité de Lyapunov pour montrer la stabilité pratique de ces derniers pour des valeurs suffisamment grandes du gain d'interconnexionThis thesis is devoted to the analysis of synchronization in large networks of heterogeneous nonlinear oscillators using tools and methods issued from control theory. We consider two models of networks; namely, the Kuramoto model which takes into account only phase coordinates of the oscillators and networks composed of nonlinear Stuart-Landau oscillators interconnected by linear coupling. For the Kuramoto model we construct an auxiliary linear system that preserves information on the natural frequencies and interconnection gains of the original Kuramoto model. We show next that existence of phase locked solutions of the Kuramoto model is equivalent to the existence of such a linear system with certain properties. This system is used to formulate conditions that ensure existence of phase-locked solutions and their stability for particular structures of network interconnections. Next, this analysis is extended to the case where both attractive and repulsive interactions are present in the network that is we consider the situation where some of the interconnection gains are allowed to be negative. In the context of networks of Stuart-Landau oscillators, we present a new coordinate transformation of the network which allows to split the network model into two parts, one describing behaviour of an "averaged" network oscillator and the second one, describing dynamics of the synchronization errors relative to this "averaged" oscillator. This transformation allows us to characterize properties of the network in terms of stability of synchronization errors and limit cycle of the "averaged" oscillator. To do so, we recast this problem as a problem of stability of compact sets and use Lyapunov stability tools to ensure practical stability of both sets for sufficiently large values of the coupling strength
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Oukil, Walid. "Systèmes couplés et morphogénèse auto-organisation de systèmes biologiques." Electronic Thesis or Diss., Bordeaux, 2016. http://www.theses.fr/2016BORD0459.
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On s’intéresse dans cette thèse à des systèmes couplés de type champ moyen en étudiant l’existence de l’état de synchronisation qui se caractérise par une distance uniformément bornée dans le temps entre chaque paire de composantes d’une solution. L’étude se base sur une méthode perturbative. Néanmoins les résultats obtenus ne sont pas évidents dans le cas non-perturbé. En outre dans le cas où le système couplé est périodique et grâce au Théorème du point fixe on montre l’existence d’une solution périodique sur le tore. L’étude de stabilité et de stabilité exponentielle est établie dans le cas linéaire et appliquée à ce type de systèmes couplésWe study in this thesis a class of a perturbed interconnected mean-field system, also known as a coupled systems. Under some assumptions we prove the existence of an invariant open set by the flow of the perturbed system ; in other word, we prove that the distance between the components of an orbit is uniformly bounded, this property is also called synchronization. We use the perturbation method to obtain the result. However the result is not trivial for the not perturbed system. We use the fixed point theorem to prove the existence of a periodic orbit in the torus. We study in addition the stability and the exponential stability of such systems by studying the stability of a linear systems
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Pinto, Pedro Dias. "Transição de fase no modelo de Kuramoto." reponame:Repositório Institucional da UnB, 2011. http://repositorio.unb.br/handle/10482/8786.
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Uma vasta gama de fenômenos na natureza exibe comportamento de sincronização. Muitas características de sincronização podem ser obtidas por meio de osciladores de fase acoplados. O estudo de osciladores acoplados foi impulsionado por Winfree e posteriormente simplificado por Kuramoto. Neste trabalho estuda-se a transição de fase no modelo de Kuramoto com e sem ruído, considerando as influências dos efeitos de tamanho finito e das distribuições de frequências naturais dos osciladores. Variando o número de osciladores interagentes, é verificada a maneira como propriedades importantes para caracterizar o regime sincronizado convergem para os valores teóricos obtidos no limite termodinâmico. É mostrado que o modo como as frequências naturais são distribuidas define o tipo de transição do modelo. O cálculo da flutuação do parâmetro de ordem na região de transição é proposto para obtenção do acoplamento crítico em grande grupos de osciladores interagentes; este método é útil pois permite estimar o acoplamento crítico de modelos cujas soluções analíticas não são possíveis. ________________________________________________________________________________ ABSTRACT
A broad range of phenomena shows synchronization behavior. Many features of the synchronization can be obtained on phase coupled oscillators. The studying of coupled oscillators was started by Winfree and later simpli ed by Kuramoto. In this work is studied the phase transition in the Kuramoto's model with and without noise, considering in uences from nite-size e ects and natural frequencies distributions of the oscillators. By changing the number of interacting oscillators, it is veri ed how important properties that characterize synchronized states converge towards the theoretical values, which are obtained in the thermodynamical limit. It is also shown how natural frequencies distributions de ne the transition type of the model. It is proposed the use of the order parameter uctuation calculation for obtaining the critical coupling on large groups of interacting oscillators; this method is useful since it allows an estimation of the critical coupling coefficient of models in which analytical solutions are not possible.
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Raboanary, Julien. "Contribution a l'analyse mathemaique du modele de kuramoto-sivashinsky." Toulon, 1990. http://www.theses.fr/1990TOUL0001.
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Le modele considere dans cette these comporte une equation aux derivees partielles spatio-temporelles (d'ordre quatre en espace, parabolique non lineaire) caracterisee en outre par un terme de diffusion negative. Il apparait dans divers contextes physico-chimiques (phenomenes d'instabilites interfaciales, turbulence de phase, front de flamme. . . ). Depuis douze ans, ce modele a ete tres etudie dans sa version unidimensionnelle. Pour l'analyse du modele multidimensionnel, la question d'existence de slution rstait encore ouverte: la presente these y repond en developpant l'indispensable recherche d'inegalites a priori. La memoire est divisee en deux parties: la premiere pour etudier le modele stabilise par l'introductin d'un terme d'ordre zero, nous y obtenons des theoremes d'existence globale pourvu que les conditions initiales soient de taille petite; la seconde partie analyse le probleme non stabilise, nous y obtenons des theoremes d'existence locale. Il s'agit de solutions fortes construites par une analyse du point fixe fondee sur des resultats classiques de semi-groupe, et une technique de majoration probablement innovante
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Tilles, Paulo Fernando Coimbra [UNESP]. "Um estudo sobre sincronização no modelo de Kuramoto." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/102550.
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Este texto é dedicado ao estudo do fenômeno de sincronização no modelo de Kuramoto. Na primeira parte o foco reside na formulação original do modelo no limite termodinâmico de infinitos osciladores e na descrição da transição para a sincronização e estabilidade das soluções em sistemas com número finito de elementos. Mostra-se também que o acoplamento crítico de sincronização 'K IND s' é determinado por um par de equações, e a solução para um caso especial com simetria na configuração de frequências naturais é obtida de forma perturbativa. A segunda parte do texto é focada na descrição do modelo de Kuramoto com acoplamento local em 1 dimensão com condições periódicas de contorno. A estrutura de árvores de sincronização média é descrita, onde ocorrem transições entre regimes caóticos e periódicos dos movimentos individuais dos osciladores. A iminência da sincronização é explorada através uma série de aproximações que mostram o comportamento crítico característico de uma bifurcação sela-nó responsável pela sincronização. A partir da definição de uma função na região sincronizada é mostrado que o acoplamento crítico de sincronização é obtido exatamente através da minimização dessa função. Através de uma sequência de exemplos de configurações com simetria é mostrado que a região sincronizada do sistema apresenta uma estrutura de múltiplas soluções estáveis, sendo a sua caracterização, análise de estabilidade e descrição das bifurcações realizada para o caso com frequências aleatórias arbitrariamente distribuídas
This text is devoted to the study of the synchronization phenomena in the Kuramoto model. In its first part the focus lies on its original formulation of infinitely many oscillators and on the description of the synchronization transition and solutions’ stability for systems with a finite number of elements. It is shown that a pair of equations characterize the critical synchronization coupling Ks, and the solution for a special case with symmetry on its natural frequencies configuration is obtained in a perturbatively way. The second part of the text is focused on the 1-dimensional Kuramoto model with periodic boundary conditions. The synchronization tree structure is described, where it is observed several transitions between chaotic and periodic regimes among the individual oscillators. The onset on synchronization is explored through a series of approximations that show the characteristic critical behavior of a saddle node bifurcation, which is responsible for the synchronization. By defining a function on the synchronized region it is shown that the critical synchronization coupling is exactly determined by the function’s minimization process. Through a sequence of examples with symmetry on its configurations it is shown that the synchronized region presents a structure of multiple stable solutions. Its complete characterization, stability analysis and bifurcations’ description is carried through for the case with randomly distributed natural frequencies
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Tilles, Paulo Fernando Coimbra. "Um estudo sobre sincronização no modelo de Kuramoto /." São Paulo : [s.n.], 2011. http://hdl.handle.net/11449/102550.
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Orientador: Gerson FranciscoCoorientador: Fernando Fagundes Ferreira
Banca: Mauro Copelli
Banca: Ricardo Luiz Viana
Banca: Paulo Laerte Natti
Banca: Tiago Pereira da Silva
Resumo: Este texto é dedicado ao estudo do fenômeno de sincronização no modelo de Kuramoto. Na primeira parte o foco reside na formulação original do modelo no limite termodinâmico de infinitos osciladores e na descrição da transição para a sincronização e estabilidade das soluções em sistemas com número finito de elementos. Mostra-se também que o acoplamento crítico de sincronização 'K IND s' é determinado por um par de equações, e a solução para um caso especial com simetria na configuração de frequências naturais é obtida de forma perturbativa. A segunda parte do texto é focada na descrição do modelo de Kuramoto com acoplamento local em 1 dimensão com condições periódicas de contorno. A estrutura de árvores de sincronização média é descrita, onde ocorrem transições entre regimes caóticos e periódicos dos movimentos individuais dos osciladores. A iminência da sincronização é explorada através uma série de aproximações que mostram o comportamento crítico característico de uma bifurcação sela-nó responsável pela sincronização. A partir da definição de uma função na região sincronizada é mostrado que o acoplamento crítico de sincronização é obtido exatamente através da minimização dessa função. Através de uma sequência de exemplos de configurações com simetria é mostrado que a região sincronizada do sistema apresenta uma estrutura de múltiplas soluções estáveis, sendo a sua caracterização, análise de estabilidade e descrição das bifurcações realizada para o caso com frequências aleatórias arbitrariamente distribuídas
Abstract: This text is devoted to the study of the synchronization phenomena in the Kuramoto model. In its first part the focus lies on its original formulation of infinitely many oscillators and on the description of the synchronization transition and solutions' stability for systems with a finite number of elements. It is shown that a pair of equations characterize the critical synchronization coupling Ks, and the solution for a special case with symmetry on its natural frequencies configuration is obtained in a perturbatively way. The second part of the text is focused on the 1-dimensional Kuramoto model with periodic boundary conditions. The synchronization tree structure is described, where it is observed several transitions between chaotic and periodic regimes among the individual oscillators. The onset on synchronization is explored through a series of approximations that show the characteristic critical behavior of a saddle node bifurcation, which is responsible for the synchronization. By defining a function on the synchronized region it is shown that the critical synchronization coupling is exactly determined by the function's minimization process. Through a sequence of examples with symmetry on its configurations it is shown that the synchronized region presents a structure of multiple stable solutions. Its complete characterization, stability analysis and bifurcations' description is carried through for the case with randomly distributed natural frequencies
Doutor
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Luçon, Eric. "Oscillateurs couplés, désordre et synchronisation." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00709998.
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Dans cette thèse, nous étudions le modèle de synchronisation de Kuramoto et plus généralement des systèmes de diffusions interagissant en champ moyen, en présence d'un aléa supplémentaire appelé désordre. La motivation principale en est l'étude du comportement du système en grande population, pour une réalisation fixée du désordre (modèle quenched). Ce document, outre l'introduction, comporte quatre chapitres. Le premier s'intéresse à la convergence de la mesure empirique du système d'oscillateurs vers une mesure déterministe, solution d'un système d'équations aux dérivées partielles non linéaires couplées (équation de McKean-Vlasov). Cette convergence est prouvée indirectement via un principe de grandes déviations dans le cas averaged et directement dans le cas quenched, sous des hypothèses plus faibles sur le désordre. Le deuxième chapitre est issu d'un travail en commun avec Giambattista Giacomin et Christophe Poquet et concerne la régularité des solutions de l'EDP limite ainsi que la stabilité de ses solutions stationnaires synchronisées dans le cas d'un désordre faible. Les deux derniers chapitres étudient l'influence du désordre sur une population d'oscillateurs de taille finie et illustrent des problématiques observées dans la littérature physique. Nous prouvons dans le troisième chapitre un théorème central limite quenched associé à la loi des grands nombres précédente: on montre que le processus de fluctuations quenched converge, en un sens faible, vers la solution d'une EDPS linéaire. Le dernier chapitre étudie le comportement en temps long de cette EDPS, illustrant le fait que les fluctuations dans le modèle de Kuramoto ne sont pas auto-moyennantes.
Book chapters on the topic "Modèle de Kuramoto"
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Fioriti, Vincenzo, Silvia Ruzzante, Elisa Castorini, Elena Marchei, and Vittorio Rosato. "Stability of a Distributed Generation Network Using the Kuramoto Models." In Lecture Notes in Computer Science, 14–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03552-4_2.
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Feketa, Petro, Alexander Schaum, and Thomas Meurer. "Synchronization Phenomena in Oscillator Networks: From Kuramoto and Chua to Chemical Oscillators." In Springer Series on Bio- and Neurosystems, 385–406. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-36705-2_16.
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AbstractThis chapter addresses the problems of synchronization analysis in various types of oscillator networks. In particular, we derive sufficient conditions for emergence of multi-cluster formations in Kuramoto networks with dynamic coupling, prove the output-feedback synchronization of chaotic behavior in networks of Chua oscillators with nonlinear static coupling, and study the synchronization of complex spatiotemporal patterns in coupled infinite-dimensional reaction-diffusion models of chemical oscillators. The obtained results contribute towards a deeper understanding of the internal organization of oscillator networks, explain the prerequisites for the emergence of patterns of synchrony and justify their stability properties in terms of the dynamical characteristics of oscillators, parameters of couplings, and the interconnection topology of the network. The interplay of these three ingredients is required for the complex and dynamically rich behavior of the network. Theoretical results of the chapter are supplemented with numerical case studies.
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Soleimani, Javad, Reza Farhangi, Gunes Karabulut Kurt, and Fatemeh Mechershavi. "Analytical Analysis of Power Network Stability: Necessary and Sufficient Conditions." In ICT for Smart Grid - Recent Advances, New Perspectives, and Applications [Working Title]. IntechOpen, 2024. http://dx.doi.org/10.5772/intechopen.1003734.
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The investigation of the synchronization of Kuramoto oscillators is a crucial applied model for studying harmonization in oscillating phenomena across physical, biological, and engineering networks. This chapter builds on previous studies by exploring the synchronization of Kuramoto oscillators while also conforming to more realistic models. Using the LaSalle Invariance Principle and contraction property, we introduce the necessary and sufficient conditions for frequency synchronization and phase cohesiveness. The novelty of this chapter’s contents lies in three key areas: First, we consider a heterogeneous second-order model with non-uniformity in coupling topology. Second, we apply a non-zero and non-uniform phase shift in coupling function. Third, we introduce a new Lyapunov-based stability analysis technique. Our findings demonstrate that heterogeneity in the network and the phase shift in the coupling function are key factors in network synchronization. We present the synchronization conditions based on network graph-theoretical characteristics and the oscillators’ parameters. Analysis of the results reveals that an increase in the phase shift and heterogeneity of oscillators will complicate the synchronization conditions. Numerical simulations confirm the validity of our theoretical results. One of the main applications of this study is the development of stability conditions for smart grids with Lossy-Power Network.
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Schulman, L. S. "Biological sciences." In When Things Grow Many, 140–79. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198861881.003.0010.
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Abstract Synchronization is important in biology, from heart beats to firefly mating. But those are not the only phenomena that become simpler as the number of constituents increases. Integrate and fire models as well as the Kuramoto theory are studied. Ants and biorobotics are similar to---of all things---glass. Systems that show power laws are genes and neural matter, both products of evolution. Emergent behavior is displayed in flocks of birds, fish, and other animals. Ecology uses maximum entropy methods to predict the number of species in a given area and other features. In some cases computers are used in agent-based modelling, in others analytic methods are used, and finally sometimes it takes both.
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Elezgaray, Juan, Gal Berkooz, Harry Dankowicz, Philip Holmes, and Mark Myers. "Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation." In Multiscale Wavelet Methods for Partial Differential Equations, 441–71. Elsevier, 1997. http://dx.doi.org/10.1016/s1874-608x(97)80013-1.
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Nolte, David D. "Network Dynamics." In Introduction to Modern Dynamics, 207–42. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198844624.003.0007.
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A language of nodes and links, degree and moments, and adjacency matrix and distance matrix, among others, is defined and used to capture the wide range of different types and properties of network topologies. Regular graphs and random graphs have fundamentally different connectivities that play a role in dynamic processes such as diffusion and synchronization on a network. Three common random graphs are the Erdös–Rényi (ER) graph, the small-world (SW) graph, and the scale-free (SF) graph. Random graphs give rise to critical phenomena based on static connectivity properties, such as the percolation threshold, but also exhibit dynamical thresholds for the diffusion of states across networks and the synchronization of oscillators. The vaccination threshold for diseases propagating on networks and the global synchronization transition in the Kuramoto model are examples of dynamical processes that can be used to probe network topologies.
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"Parabolic Equations in One Dimension: Thin Film, Kuramoto-Sivashinsky, and Magma Models." In Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, 128–93. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420011623-9.
Full textConference papers on the topic "Modèle de Kuramoto"
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Wenxue Wang and Bijoy Ghosh. "Kuramoto Models, Coupled Oscillations and laser networks." In SICE Annual Conference 2007. IEEE, 2007. http://dx.doi.org/10.1109/sice.2007.4420964.
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Wenxue Wang and B. K. Ghosh. "Detection of depth in binocular visual systems using Kuramoto models." In 2006 American Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/acc.2006.1656557.
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Gall, Walter, Ying Zhou, and Joseph Salisbury. "Synchronization of a Network With Piecewise-Linear Dynamics." In ASME 2010 Dynamic Systems and Control Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/dscc2010-4230.
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We consider two and three phase-oscillators as in the Kuramoto model of coupled oscillators, replacing the sine wave interaction with a sawtooth wave. We show that for the case of non-uniform input-symmetric coupling strengths, the non-smooth, piecewise-linear dynamics synchronizes when the coupling strengths are large enough to overcome the differences in the natural frequencies of the oscillators. Stability is analyzed separately in the regions where the dynamics is linearized. These regions are separated by the switching boundaries where the vector field is discontinuous.
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Demetriou, Michael A. "Adaptive alternatives in the velocity control of Mean-Field Kuramoto Models." In 2023 American Control Conference (ACC). IEEE, 2023. http://dx.doi.org/10.23919/acc55779.2023.10156040.
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Xu, Qing, Shitao Wang, Jiayi Liu, Huihui Song, and Yanbin Qu. "Analysis of Kuramoto models for AC microgrids based on droop control." In 2022 IEEE Sustainable Power and Energy Conference (iSPEC). IEEE, 2022. http://dx.doi.org/10.1109/ispec54162.2022.10033040.
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Liu, Zhao, and Ziang Zhang. "Quantifying transient stability of generators by basin stability and Kuramoto-like models." In 2017 North American Power Symposium (NAPS). IEEE, 2017. http://dx.doi.org/10.1109/naps.2017.8107260.
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Ajala, Olaoluwapo, Nathan Baeckeland, Sairaj Dhople, and Alejandro Dominguez-Garcia. "Uncovering the Kuramoto Model from Full-order Models of Grid-forming Inverter-based Power Networks." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683125.
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Klein, Daniel J., Phillip Lee, Kristi A. Morgansen, and Tara Javidi. "Integration of communication and control using discrete time Kuramoto models for multivehicle coordination over broadcast networks." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434294.
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Gopakumar, Ramachandran, Rahul Belur Vishwanath, Jasmeet Singh, Ankit Dutta, and Swetaprovo Chaudhuri. "On the Dynamics of Instability Mitigation by Actuating Swirler Motion in a Lean Premixed Turbulent Combustor." In ASME 2017 Gas Turbine India Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gtindia2017-4710.
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In this paper, we present a novel initial attempt on analysis of the mitigation mechanism of instability by rotating the otherwise static swirler in a lean premixed, swirl stabilized, labscale combustor. It has been reported in our previous work that increasing the swirler rotation rate mitigates the self-excited thermoacoustic instability in a model lab-scale combustor, over a range of conditions. Here, it is found that for a given period of observation, instead of a continuous and gradual decrease in the time localized pressure amplitude from the fully unstable state towards the fully mitigated state, the fraction of the time during which instability is present is reduced. With increasing swirler rotation rates, the instability becomes more intermittent with progressive reduction in frequency of their occurrence. High speed PIV results are also presented along with simultaneous pressure signals which support this claim. Such an intermittent route to instability mitigation could be attributed to the background turbulent flow field and is reminiscent of the intermittent opposite transition (implemented by changing the Reynolds number) from a fully chaotic state to a fully unstable state as recently discovered in Nair, Thampi and Sujith [1]. An attempt is made to model the behavior of pressure oscillations using the well established mean-field Kuramoto model. The variation of the order parameter r, which is the parameter for the measurement of synchronization between the oscillators provides critical insights on the transition from the unstable, intermittent to stable states.
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Ferreira, Maria Teodora, Celso B. N. Freitas, Margarete O. Domingues, and Elbert E. N. Macau. "Modelo de kuramoto e a verificacção da diferenc¸a de fase usando uma metodologia baseada na transformada wavelet complexa dual-tree : resultados preliminares." In DINCON 2013 – Conferência Brasileira de Dinâmica, Controle e Aplicações. SBMAC, 2013. http://dx.doi.org/10.5540/03.2013.001.01.0127.
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