The time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons is investigated in this paper. The time-delay influence on the structure of the slow manifold is first studied by using the method of stability switch. And then on the basis of the geometric singular perturbation theory, case studies are given to show that the time delay can suppress the bursting o...

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of th...

Tunable dual-frequency oscillation is demonstrated in a vertical external-cavity surface-emitting laser. Simultaneous and robust oscillation of the two orthogonally polarized eigenstates is achieved by reducing their overlap in the optical active medium. The class-A dynamics of this laser, free of relaxation oscillations, enables one to suppress the electrical phase noise in excess that is usua...

This paper presents a laser model for describing the effects of nonequilibrium carrier distributions. The approach is based on the coupled Maxwell-semiconductor-Bloch equations, with carrier–carrier and carrier–phonon collisions treated in the relaxation rate approximation. Using examples involving relaxation oscillation, current modulation, and optical injection, we demonstrate how the model c...

Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) r...

Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films. We show that the FOs at the Pb(111) surface decay as 1/x with the distance x from the surface, different from the conventional 1/x(2) power law at other ...

If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on friction or dissipation in the material. We call this effect "relaxation damping". The rate of energy dissipation due to relaxation damping is calculated in a clos...

It is commonly believed that task performance is improved by listening to Mozart’s music. Although this so-called Mozart effect is not often discussed in scientific literatures, those psychological experiments that have addressed it tend to confirm its existence. For example, college students who listened to Mozart’s Sonata KV.448 scored 8 to 9 points higher on the IQ test than students who had...

We give a pedagogical introduction to the attractor mechanism. We begin by developing the formalism for the simplest example of spherically symmetric black holes in five dimensions which preserve supersymmetry. We then discuss the refinements needed when spherical symmetry is relaxed. This is motivated by rotating black holes and, especially, black rings. An introduction to nonBPS attractors is...