68 research outputs found
Adaptive dynamical networks
It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks
Critical Switching in Globally Attractive Chimeras
We report on a new type of chimera state that attracts almost all initial
conditions and exhibits power-law switching behavior in networks of coupled
oscillators. Such switching chimeras consist of two symmetric configurations,
which we refer to as subchimeras, in which one cluster is synchronized and the
other is incoherent. Despite each subchimera being linearly stable, switching
chimeras are extremely sensitive to noise: arbitrarily small noise triggers and
sustains persistent switching between the two symmetric subchimeras. The
average switching frequency scales as a power law with the noise intensity,
which is in contrast with the exponential scaling observed in typical
stochastic transitions. Rigorous numerical analysis reveals that the power-law
switching behavior originates from intermingled basins of attraction associated
with the two subchimeras, which in turn are induced by chaos and symmetry in
the system. The theoretical results are supported by experiments on coupled
optoelectronic oscillators, which demonstrate the generality and robustness of
switching chimeras
The Kuramoto model in complex networks
181 pages, 48 figures. In Press, Accepted Manuscript, Physics Reports 2015 Acknowledgments We are indebted with B. Sonnenschein, E. R. dos Santos, P. Schultz, C. Grabow, M. Ha and C. Choi for insightful and helpful discussions. T.P. acknowledges FAPESP (No. 2012/22160-7 and No. 2015/02486-3) and IRTG 1740. P.J. thanks founding from the China Scholarship Council (CSC). F.A.R. acknowledges CNPq (Grant No. 305940/2010-4) and FAPESP (Grants No. 2011/50761-2 and No. 2013/26416-9) for financial support. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP).Peer reviewedPreprin
Towards a continuous dynamic model of the Hopfield theory on neuronal interaction and memory storage
The purpose of this work is to study the Hopfield model for neuronal
interaction and memory storage, in particular the convergence to the stored
patterns. Since the hypothesis of symmetric synapses is not true for the
brain, we will study how we can extend it to the case of asymmetric
synapses using a probabilistic approach. We then focus on the description
of another feature of the memory process and brain: oscillations. Using the
Kuramoto model we will be able to describe them completely, gaining the
presence of synchronization between neurons. Our aim is therefore to
understand how and why neurons can be seen as oscillators and to establish
a strong link between this model and the Hopfield approach
Sincronização induzida por forças externas em redes modulares
Orientador: Marcus Aloizio Martinez de AguiarTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: Neste trabalho estudamos a sincronização de osciladores de Kuramoto sujeitos a forças externas em redes modulares complexas. A motivação está na dinâmica neuronal que ocorre durante o processamento de informação no córtex cerebral que parece estar relacionada ao disparo síncrono de grupos de neurônios. A organização dos neurônios é modular, com agrupamentos associados a diferentes funções e estruturas cerebrais, e precisa responder constantemente a estímulos externos. Anormalidades no processo de sincronização, como a ativação de múltiplos módulos têm sido associadas à doenças como epilepsia e Alzheimer. Nesse contexto, estudamos o comportamento de osciladores de Kuramoto forçados, onde apenas uma fração deles é submetida a uma força externa periódica. Quando todos os osciladores recebem o estímulo externo o sistema sempre sincroniza com a força externa se a sua intensidade for suficientemente grande. Mostramos que as condições para a sincronização global dependem da fração de nós forçada e da topologia da rede e das intensidades do acoplamento interno e da força externa. Desenvolvemos cálculos numéricos e analíticos para a força crítica que leva a rede à sincronização global em função da fração de osciladores forçados. Como uma aplicação estudamos a resposta da rede de junções elétricas do \textit{C. elegans} ao estímulo externo usando o modelo de Kuramoto parcialmente forçado, aplicando a força a grupos específicos de neurônios. Os estímulos foram aplicados a três módulos topológicos, dois gânglios, especificados por sua localização anatômica, e aos grupos funcionais compostos por todos os neurônios sensoriais e motores. Encontramos que os módulos topológicos não contêm grupos puramente anatômicos ou classes funcionais e que estimular diferentes classes neuronais leva a respostas muito diferentes, medidas em termos de sincronização e correlações de velocidade de fase. Em todos os casos a estrutura modular impede a sincronização global, protegendo o sistema de falhas. As respostas aos estímulos aplicados aos módulos topológicos e funcionais mostram padrões pronunciados de correlação ou anti-correlação com outros módulos que não foram observados quando o estímulo foi aplicado a um gânglio com neurônios funcionais mistos. Todos os códigos e dados utilizados nesta tese estão disponível em [1]Abstract: In this work we study the synchronization of Kuramoto oscillators driven by external forces in complex modular networks. The motivation is the neuronal dynamics that takes place during information processing in the neural cortex, which seems to be related to the synchronous firing of groups of neurons. The neuron organization is modular, with clusters associated to different functions and brain structures, and need to constantly respond to external stimuli. Abnormalities in the process of synchronization, such as the activation of multiple modules, have been associated with epilepsy and Alzheimer's disease. In this context, we study the behavior of forced Kuramoto oscillators where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. We show that the conditions for global synchronization depend on the fraction of nodes being forced and on network topology, strength of internal couplings and intensity of external forcing. We develop numerical and analytical calculations for the critical force for global synchronization as a function of the fraction of forced oscillators. As an application we study the response of the electric junction \textit{C. elegans} network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to three topological modules, two ganglia, specified by their anatomical localization, and to the functional groups composed of all sensory and motoneurons. We found that topological modules do not contain purely anamotical groups or functional classes, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases the modular structure hindered full synchronization, protecting the system from seizures. The responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to a ganglion with mixed functional neurons. All codes and data used in this thesis are available in [1]DoutoradoFísicaDoutora em Ciências141021/2017-9CNP
Perspectives on adaptive dynamical systems
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches
Automatic synchronisation of the cell cycle in budding yeast through closed-loop feedback control
The cell cycle is the process by which eukaryotic cells replicate. Yeast cells cycle asynchronously with each cell in the population budding at a different time. Although there are several experimental approaches to synchronise cells, these usually work only in the short-term. Here, we build a cyber-genetic system to achieve long-term synchronisation of the cell population, by interfacing genetically modified yeast cells with a computer by means of microfluidics to dynamically change medium, and a microscope to estimate cell cycle phases of individual cells. The computer implements a controller algorithm to decide when, and for how long, to change the growth medium to synchronise the cell-cycle across the population. Our work builds upon solid theoretical foundations provided by Control Engineering. In addition to providing an avenue for yeast cell cycle synchronisation, our work shows that control engineering can be used to automatically steer complex biological processes towards desired behaviours similarly to what is currently done with robots and autonomous vehicles
Perspectives on adaptive dynamical systems
Adaptivity is a dynamical feature that is omnipresent in nature,
socio-economics, and technology. For example, adaptive couplings appear in
various real-world systems like the power grid, social, and neural networks,
and they form the backbone of closed-loop control strategies and machine
learning algorithms. In this article, we provide an interdisciplinary
perspective on adaptive systems. We reflect on the notion and terminology of
adaptivity in different disciplines and discuss which role adaptivity plays for
various fields. We highlight common open challenges, and give perspectives on
future research directions, looking to inspire interdisciplinary approaches.Comment: 46 pages, 9 figure
From Dynamics to Structure of Complex Networks: Exploiting Heterogeneity in the Sakaguchi-Kuramoto Model
[eng] Most of the real-world complex systems are best described as complex networks and can be mathematically described as oscillatory systems, coupled with the neighbours through the connections of the network. The flashing of fireflies, the neuronal brain signals or the energy flow through the power grid are some examples. Yoshiki Kuramoto came up with a tractable mathematical model that could capture the phenomenology of collective synchronization by suggesting that oscillators were coupled by a sinusoidal function of their phase differences. Later, Yoshiki Kuramoto together with Hidetsugu Sakaguchi presented a generalization of the previous limit-cycle set of oscillators Kuramoto’s model which incorporated a constant phase lag between oscillators. Subsequent studies of the model included the network structure within the model together with the global shift. For a wide range of the phase lag values, the system becomes synchronized to a resulting frequency, i.e., the dynamics reaches a stationary state.
In the original work of Kuramoto and Sakaguchi and in most of the consequent later studies, a uniform distribution of phase lag parameters is customarily assumed. However, the intrinsic properties of nodes – that assuredly represent the constituents of real systems – do not need be identical but distributed non-homogeneously among the population. This thesis contributes to the understanding of the Kuramoto-Sakaguchi model with a generalization for nonhomogeneous phase lag parameter distribution. Considering different scenarios concerning the distribution of the frustration parameter among the oscillators represents a major step towards the extension of the original model and provides significant novel insights into the structure and function of the considered network.
The first setting that the present thesis considers consists in perturbing the stationary state of the system by introducing a non-zero phase lag shift into the dynamics of a single node. The aim of this work is to sort the nodes by their potential effect on the whole network when a change on their individual dynamics spreads over the entire oscillatory system by disrupting the otherwise synchronized state. In particular, we define functionability, a novel centrality measure that addresses the question of which are the nodes that, when individually perturbed, are best able to move the system away from the fully synchronized state. This issue may be relevant for the identification of critical nodes that are either beneficial – by enabling access to a broader spectrum of states – or harmful – by destroying the overall synchronization.
The second scenario that the present thesis addresses considers a more general configuration in which the phase lag parameter is an intrinsic property of each node, not necessarily zero, and hence exploring the potential heterogeneity of the frustration among oscillators. We obtain the analytical
solution of frustration parameters so as to achieve any phase configuration, by linearizing the most general model. We also address the fact that the question ’among all the possible solutions, which is the one that makes the system achieve a particular phase configuration with the minimum required cost?’ is of particular relevance when we consider the plausible real nature of the system.
Finally, the homogenous distribution of phase lag parameters is revisited in the last scenario. As studied in the literature, a certain degree of symmetry is an attribute of real-world networks. Nevertheless, beyond structural or topological symmetry, one should consider the fact that real- world networks are exposed to fluctuations or errors, as well as mistaken insertions or removals. In the present thesis, we provide an alternative notion to approximate symmetries, which we call ‘Quasi-Symmetries’ and are defined such that they remain free to impose any invariance of a particular network property and are obtained from the stationary state of the Kuramoto-Sakaguchi model with a homogeneous phase lag distribution. A first contribution is exploring the distributions of structural similarity among all pairs of nodes. Secondly, we define the ‘dual network’, a weighted network –and its corresponding binarized counterpart– that effectively encloses all the information of quasi-symmetries in the original one.[cat] La major part dels sistemes complexos presents en la natura i la societat es poden descriure com a xarxes complexes. Molts d’aquests sistemes es poden modelitzar matemàticament com un sistema oscil·latori, on les unitats queden acoblades amb els components veïns a través de les connexions de la xarxa. Yoshiki Kuramoto i Hidetsugu Sakaguchi van presentar la generalització del ben conegut model d’oscil·ladors de Kuramoto, on s’incorporava un terme de desfasament entre parelles d’oscil·ladors. Aquesta tesi contribueix en la comprensió d’aquest model, tot considerant una distribució no homogènia d’aquest paràmetre de desfasament o frustració. S’han considerat tres escenaris diferents, tots ells donant lloc a resultats que permeten una millor descripció de l’estructura i funció de la xarxa que s’està considerant.
Una primera configuració consisteix en pertorbar l’estat estacionari tot introduint un desfasament en la dinàmica d’un node de manera aïllada. Seguidament, definim la funcionabilitat, una mesura de centralitat única que respon a la pregunta de, quins nodes, quan són pertorbats individualment, són més capaços d’allunyar el sistema de l’estat sincronitzat. Aquest fet podria suposar un comportament beneficiós o perjudicial per sistemes reals.
El segon escenari considera la configuració més flexible, explorant la potencial heterogeneïtat dels paràmetres de frustració dels diferents nodes. Obtenim la solució analítica d’aquesta distribució per tal d’assolir qualsevol configuració de les fases dels oscil·ladors, a través de la linearització del model. També contestem a la pregunta: “de totes les possibles solucions, quina és la que implica un menor cost per tal d’assolir una configuració en particular?”.
Finalment, en l’últim escenari, proporcionem una definició alternativa al concepte de simetria aproximada d’una xarxa, i que anomenem “Quasi simetries”. Aquestes són definides sense imposar invariàncies en les propietats del sistema, sinó que s’obtenen de l’estat estacionari del model de Kuramoto-Sakaguchi model, tot considerant una distribució homogènia dels paràmetres de frustració
- …