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Concept

Modèle de Kuramoto

Publications associées (23)

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

Modeling synchronization in globally coupled oscillatory systems using model order reduction

Jan Sickmann Hesthaven, Niccolo' Discacciati

We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suita ...

American Institute of Physics2021

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators

Auke Ijspeert, Ludovic Righetti, Jonas Buchli

Oscillators have two main limitations: their synchronization properties are limited (i.e., they have a finite synchronization region) and they have no memory of past interactions (i.e., they return to their intrinsic frequency whenever the entraining signa ...

SIAM PUBLICATIONS2021

Optogenetic Interrogation of Circuits Following Neurotrauma

Grégoire Courtine, Steven Lee Ceto

Biological and engineering strategies for neural repair and recovery from neurotrauma continue to emerge at a rapid pace. Until recently, studies of the impact of neurotrauma and repair strategies on the reorganization of the central nervous system have fo ...

FRONTIERS MEDIA SA2021

Modeling time-varying brain networks with a self-tuning optimized Kalman filter

Gijs Plomp, David Pascucci

Brain networks are complex dynamical systems in which directed interactions between different areas evolve at the sub-second scale of sensory, cognitive and motor processes. Due to the highly non-stationary nature of neural signals and their unknown noise ...

2020

Learning Hawkes Processes Under Synchronization Noise

Patrick Thiran, Matthias Grossglauser, Negar Kiyavash, Seyed Jalal Etesami, William Trouleau

Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of lear ...

PMLR2019

Single Neuron Optimization as a Basis for Accurate Biophysical Modeling : The Case of Cerebellar Granule Cells

Felix Schürmann, Werner Alfons Hilda Van Geit

In realistic neuronal modeling, once the ionic channel complement has been defined, the maximum ionic conductance (Gi-max) values need to be tuned in order to match the firing pattern revealed by electrophysiological recordings. Recently, selection/mutatio ...

Frontiers Media Sa2017

Coevolution of Synchronization and Cooperation in Costly Networked Interactions

Alessio Vincenzo Cardillo

Despite the large number of studies on synchronization, the hypothesis that interactions bear a cost for involved individuals has seldom been considered. The introduction of costly interactions leads, instead, to the formulation of a dichotomous scenario i ...

American Physical Society2017

Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity

Patric Hagmann

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. ...

Public Library Science2015

Multi-timescale Modeling of Activity-Dependent Metabolic Coupling in the Neuron-Glia-Vasculature Ensemble

Pierre Magistretti, Igor Allaman, Renaud Jolivet, Jay Coggan

Glucose is the main energy substrate in the adult brain under normal conditions. Accumulating evidence, however, indicates that lactate produced in astrocytes (a type of glial cell) can also fuel neuronal activity. The quantitative aspects of this so-calle ...

2015

Inference of neuronal network spike dynamics and topology from calcium imaging data

Wulfram Gerstner, Joao Emanuel Felipe Gerhard, Friedemann Zenke

Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence ("spike trains") from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR ...

Frontiers Research Foundation2013

Multistability of twisted states in non-locally coupled Kuramoto-type models

Martin Hasler

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sig ...

American Institute of Physics2012

Doesspike-timing-dependent synaptic plasticity couple or decouple neurons firing in synchrony?

Marc-Oliver Gewaltig

Spike synchronization is thought to have a constructive role for feature integration, attention, associative learning, and the formation of bidirectionally connected Hebbian cell assemblies. By contrast, theoretical studies on spike-timing-dependent plasti ...

Frontiers Res Found2012

Non-normal amplification in random balanced neuronal networks

Wulfram Gerstner, Guillaume Hennequin, Tim Vogels

In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activit ...

2012

Lossy source coding via spatially coupled LDGM ensembles

Rüdiger Urbanke, Nicolas Macris, Marc Vuffray, Vahid Aref

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generatormatrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of ...

Ieee2012

Self-Adaptive Attractor-Shaping for Oscillators Networks

Max-Olivier Hongler, Julio Rodriguez, Philippe Blanchard

We consider a network of N coupled limit cycle oscillators, each having a set of control parameters Λ_k, k = 1, . . . , N, that controls the frequency and the geometry of the limit cycle. We implement a self-adaptive mechanism that drives the local systems ...

2011

Phase-based features for Motor Imagery Brain-Computer Interfaces

José del Rocio Millán Ruiz, Robert Leeb, Michele Tavella

Motor imagery (MI) brain-computer interfaces (BCIs) translate a subject’s motor intention to a command signal. Most MI BCIs use power features in the mu or beta rhythms, while several results have been reported using a measure of phase synchrony, the phase ...

IEEE2011

Mesoscale and clusters of synchrony in networks of bursting neurons

Martin Hasler, Igor Belykh

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demo ...

American Institute of Physics2011

Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

Michele Giugliano

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically det ...

2011

Hyperbolic angular statistics for globally coupled oscillators

Max-Olivier Hongler, Roger Filliger, Philippe Blanchard

We analytically discuss a multiplicative noise generalization of the Kuramoto- Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean-ﬁeld limit, the resulting class of invariant measures coincides with a generalized, two-par ...

IOP Publishing - EPL Association2010