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Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the(More)
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The(More)
Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric field domains, pinning or propagation of domain walls, self-sustained oscillations of the current and chaos. Theories of these effects use reduced descriptions of(More)
A model for synchronization of globally coupled phase oscillators including " inertial " effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsyn-chronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural(More)
We present the numerical methods and simulations used to solve a charge transport problem in semiconductor physics. The problem is described by a Wigner-Poisson kinetic system we have recently proposed and whose results are in good agreement with known experiments. In this model we consider doped semiconductor superlattices in which electrons are supposed(More)
A two-time scale asymptotic method has been introduced to analyze the mul-timodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in different components corresponding to the different peaks of the oscillator frequency distribution. Each component evolves(More)
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to synchronization to phases with a time periodic order parameter. The richest behavior is found near the tricritical point were(More)
The asymptotic behavior for the Vlasov–Poisson–Fokker–Planck system in bounded domains is analyzed in this paper. Boundary conditions defined by a scattering kernel are considered. It is proven that the distribution of particles tends for large time to a Maxwellian determined by the solution of the Poisson–Boltzmann equation with Dirichlet boundary(More)
OBJECTIVE To estimate the incidence of influenza-virus-associated severe pneumonia among Salvadorian children aged < 5 years. METHODS Data on children aged < 5 years admitted with severe pneumonia to a sentinel hospital in the western region were collected weekly. Nasal and oropharyngeal swab specimens were collected from a convenience sample of case(More)
The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes " inertial " effects. This problem is relevant in the context of networks of Josephson junctions. Second, a(More)