Related papers: Classical solutions of a mean field system for pul…
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…
We recently introduced idealized mean-field models for networks of integrate-and-fire neurons with impulse-like interactions -- the so-called delayed Poissonian mean-field models. Such models are prone to blowups: for a strong enough…
This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled…
We are concerned with an elliptic problem which describes a mean field equation of the equilibrium turbulence of vortices with variable intensities. In the first part of the paper we describe the blow-up phenomenon and highlight the…
We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term.…
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
It is shown that a spin system is equivalent to a set of constrained harmonic oscillators. For finite, but large, systems, a continuous approximation to the density of states can be used, and the oscillator frequencies can be exactly…
We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…
Despite their formal simplicity, most lattice spin models cannot be easily solved, even under the simplifying assumptions of mean field theory. In this manuscript, we present a method for generating mean field solutions to classical…
In this thesis we develop methods for many-body open quantum systems and apply them to systems of organic polaritons. The methods employ a mean-field approach to reduce the dimensionality of large-scale problems. Initially assuming the…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
We present a detailed analysis of the broken-symmetry mean-field solutions using a four-electron rectangular quantum dot as a model system. Comparisons of the density-functional theory predictions with the exact ones show that the symmetry…
We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve $\mathcal{C}$, thereby maintaining the typical ordering of (identical) phase oscillators. This is…
A mean-field model to describe electron transfer processes in ion-molecule collisions at the $\hbar =0$ level is presented and applied to collisions involving water and ammonia molecules. Multicenter model potentials account for the…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
Analytic treatment of a non-equilibrium random system with large degrees of freedoms is one of most important problems of physics. However, little research has been done on this problem as far as we know. In this paper, we propose a new…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…