Browse
Submit Data
Databases
API
Help

Dataset Information

28 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs.

ABSTRACT: The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d?

SUBMITTER: Odor G

PROVIDER: S-EPMC6928153 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs.

Ódor Géza G Kelling Jeffrey J

Scientific reports 20191223 1

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < ...[more]

PMID: 31873076

Similar Datasets

Exact solution for first-order synchronization transition in a generalized Kuramoto model.

Project description:First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

| S-EPMC4248286 | biostudies-literature

Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model.

Project description:The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto model, a well-known mathematical model in non-linear dynamics. By investigating the collective dynamics in arrays of STO we find that the synchronization in such systems is a finite size effect and show that the critical coupling-for a complete synchronized state-scales with the number of oscillators. Using realistic values of the dipolar coupling strength between STO we show that this imposes an upper limit for the maximum number of oscillators that can be synchronized. Further, we show that the lack of long range order is associated with the formation of topological defects in the phase field similar to the two-dimensional XY model of ferromagnetism. Our results shed new light on the synchronization of STO, where controlling the mutual synchronization of several oscillators is considered crucial for applications.

| S-EPMC5007507 | biostudies-literature

Dynamics in the Sakaguchi-Kuramoto model with bimodal frequency distribution.

Project description:In this work, we study the Sakaguchi-Kuramoto model with natural frequency following a bimodal distribution. By using Ott-Antonsen ansatz, we reduce the globally coupled phase oscillators to low dimensional coupled ordinary differential equations. For symmetrical bimodal frequency distribution, we analyze the stabilities of the incoherent state and different partial synchronous states. Different types of bifurcations are identified and the effect of the phase lag on the dynamics is investigated. For asymmetrical bimodal frequency distribution, we observe the revival of the incoherent state, and then the conditions for the revival are specified.

| S-EPMC7725404 | biostudies-literature

Mandala networks: ultra-small-world and highly sparse graphs.

Project description:The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are robust against random failures. Furthermore, as the size of the network increases, its shortest path becomes asymptotically invariant and the density of links goes to zero, making it ultra-small world and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically. Finally, we show that some simple changes on the original network formulation can lead to an improved topology against malicious attacks.

| S-EPMC4357991 | biostudies-other

Label-based routing for a family of small-world Farey graphs.

Project description:We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.

| S-EPMC4863731 | biostudies-other

Identifying critical regions in small-world marine metapopulations.

Project description:The precarious state of many nearshore marine ecosystems has prompted the use of marine protected areas as a tool for management and conservation. However, there remains substantial debate over their design and, in particular, how to best account for the spatial dynamics of nearshore marine species. Many commercially important nearshore marine species are sedentary as adults, with limited home ranges. It is as larvae that they disperse greater distances, traveling with ocean currents sometimes hundreds of kilometers. As a result, these species exist in spatially complex systems of connected subpopulations. Here, we explicitly account for the mutual dependence of subpopulations and approach protected area design in terms of network robustness. Our goal is to characterize the topology of nearshore metapopulation networks and their response to perturbation, and to identify critical subpopulations whose protection would reduce the risk for stock collapse. We define metapopulation networks using realistic estimates of larval dispersal generated from ocean circulation simulations and spatially explicit metapopulation models, and we then explore their robustness using node-removal simulation experiments. Nearshore metapopulations show small-world network properties, and we identify a set of highly connected hub subpopulations whose removal maximally disrupts the metapopulation network. Protecting these subpopulations reduces the risk for systemic failure and stock collapse. Our focus on catastrophe avoidance provides a unique perspective for spatial marine planning and the design of marine protected areas.

| S-EPMC3203776 | biostudies-literature

Dynamics of semiflexible recursive small-world polymer networks.

Project description:One of the fundamental issues in polymer physics is to reveal the relation between the structures of macromolecules and their various properties. In this report, we study the dynamical properties of a family of deterministically growing semiflexible treelike polymer networks, which are built in an iterative method. From the analysis of the corresponding dynamical matrix we derive the solution for its eigenvalues and their multiplicities, making use of a combined numerical and analytical approach. The eigenvalue spectra allow us to investigate the mechanical relaxation forms in depth for different values of the stiffness parameter. We observe that the dynamics of semiflexible networks is sensitive to the stiffness parameter. Our work paves a way to explore the structures of the highly symmetric polymers and provides a comprehensive understanding of the role of semiflexibility for the regular treelike networks which possess a small-world feature.

| S-EPMC4271264 | biostudies-other

The mathematics of asymptotic stability in the Kuramoto model.

Project description:Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the corresponding rigorous validation has long remained problematic and was achieved only recently. This paper reviews the mathematical results on asymptotic stability of stationary solutions in the continuum limit of the Kuramoto model, and provides insights into the principal arguments of proofs. This review is complemented with additional original results, various examples, and possible extensions to some variations of the model in the literature.

| S-EPMC6304033 | biostudies-literature

Frustrated hierarchical synchronization and emergent complexity in the human connectome network.

Project description:The spontaneous emergence of coherent behavior through synchronization plays a key role in neural function, and its anomalies often lie at the basis of pathologies. Here we employ a parsimonious (mesoscopic) approach to study analytically and computationally the synchronization (Kuramoto) dynamics on the actual human-brain connectome network. We elucidate the existence of a so-far-uncovered intermediate phase, placed between the standard synchronous and asynchronous phases, i.e. between order and disorder. This novel phase stems from the hierarchical modular organization of the connectome. Where one would expect a hierarchical synchronization process, we show that the interplay between structural bottlenecks and quenched intrinsic frequency heterogeneities at many different scales, gives rise to frustrated synchronization, metastability, and chimera-like states, resulting in a very rich and complex phenomenology. We uncover the origin of the dynamic freezing behind these features by using spectral graph theory and discuss how the emerging complex synchronization patterns relate to the need for the brain to access -in a robust though flexible way- a large variety of functional attractors and dynamical repertoires without ad hoc fine-tuning to a critical point.

| S-EPMC4126002 | biostudies-other

Competitive influence maximization and enhancement of synchronization in populations of non-identical Kuramoto oscillators.

Project description:Many networked systems have evolved to optimize performance of function. Much literature has considered optimization of networks by central planning, but investigations of network formation amongst agents connecting to achieve non-aligned goals are comparatively rare. Here we consider the dynamics of synchronization in populations of coupled non-identical oscillators and analyze adaptations in which individual nodes attempt to rewire network topology to optimize node-specific aims. We demonstrate that, even though individual nodes' goals differ very widely, rewiring rules in which each node attempts to connect to the rest of the network in such a way as to maximize its influence on the system can enhance synchronization of the collective. The observed speed-up of consensus finding in this competitive dynamics might explain enhanced synchronization in real world systems and shed light on mechanisms for improved consensus finding in society.

| S-EPMC5768883 | biostudies-other

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data