Related papers: Modelling cortical network dynamics
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…
Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…
We investigate states of enhanced activity in a biological neuronal network composed of pulse-coupled oscillators. The synaptic couplings between the neurons are dynamic, modeling spike time dependent plasticity. The network exhibits…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
We study the asymptotic clustering (phase-locking) dynamics for the Kuramoto model. For the analysis of emergent asymptotic patterns in the Kuramoto flow, we introduce the pathwise critical coupling strength which yields a sharp transition…
This paper studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the $n$-torus called winding cells. Second, we analyze the semicontractivity…
In this review, we discuss critical dynamics of simple nonequilibrium models on large connectomes, obtained by diffusion MRI, representing the white matter of the human brain. In the first chapter, we overview graph theoretical and…
Drug-resistant epilepsy is traditionally characterized by pathologic cortical tissue comprised of seizure-initiating `foci'. These `foci' are thought to be embedded within an epileptic network whose functional architecture dynamically…
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…
Macroscopic studies of cortical tissue reveal a prevalence of oscillatory activity, that reflect a fine tuning of neural interactions. This research extends neural field theories by incorporating generalized oscillatory dynamics into…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
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…
We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
We consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large…
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…