Related papers: Dynamics of globally coupled oscillators: progress…
Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the…
In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena…
We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in $\mathbb{R}^d$. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
The recent progress in establishing the existence of finite neutrino masses and mixing between generations of neutrinos has been remarkable, if not astounding. The combined results from studies of atmospheric neutrinos, solar neutrinos, and…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any…
We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in…
We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
We consider an array of units each of which can be in one of three states. Unidirectional transitions between these states are governed by Markovian rate processes.The interactions between units occur through a dependence of the transition…
We overview the status of the studies on neutrino oscillations with accelerators at the present running experiments. Past and present results enlighten the path towards the observation of massive neutrinos and the settling of their…
This paper investigates the exponential stability of abstract mean field systems in their synchronized state. We analyze stability by studying the linearized system and demonstrate the existence of an exponentially stable invariant…
An overview of a microscopic framework based on the Hartree-Fock description of the mean field is presented which, starting from an effective interaction allows a description of collective motions. A study of the isotope shifts in the Pb…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Recent evidence for neutrino oscillations has revolutionized the study of neutrino masses and mixing. This report gives an overview of what we are learning from the neutrino oscillation experiments, the prospects for the near term, and the…
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…