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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)
Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress F: for |F|<F(cd) (dynamic Peierls stress), wave fronts fail to propagate, for F(cd)<|F|<F(cs) stable static and moving wave fronts coexist, and for |F|>F(cs) (static Peierls stress) there are only stable(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)
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for(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)
Charge transport in semiconductor superlattices can be described through a discrete drift-diffusion model. In this model, we identify some small parameter h > 0, by means of physically relevant dimensionless quantities. Precisely, we investigate a regime where the length of the superlattice period is small while the doping profile is high. In the limit h →(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)