In a recent paper in this Journal, [2], the authors discuss a relaxation oscillator which apparently has not been put in standard Lienard form. They use geometric perturbation theory to analyze this model. Their main result is the existence and uniqueness of a periodic solution for small values of two parameters, δ and ε, and the behavior of this solution as δ and ε tend to zero. We show how st...

The timing and magnitude of airway narrowing in central apneas is unknown. We have developed a method of apnea classification that relies on the transmission of cardiac airflow oscillation to indicate airway patency. Using a theoretical model, we showed that the amplitude of the cardiac airflow oscillation is proportional to airway diameter for small lumens. While in the majority of central apn...

The circadian system has been regarded as a limit cycle oscillator constructed by the integrated interaction of clock genes and proteins. Here, we investigated a mammalian circadian oscillation geometrically before and after a perturbation. We detected the singular point and transition from a type 1 to type 0 phase response curve (PRC) and determined the embedding dimension to show how many var...

In this paper, the nonlinear rate equations governing a quantum dot laser isused to simulate the transient as well as the steady-state behaviors of the laser.Computation results show that the rate equations are capable of simulating true behaviorof a quantum dot laser. Then, the pump rates of the rate equations (which show indirectelectrical pumping of the quantum dots through a wetting layer) ...

Detailed analyses of the short-term stability of the semiconductor fiber ring laser (SFRL) are presented. Analysis with rate equations shows that the relaxation oscillation effect does not exist in the SFRL. With a frequency-domain model, the mode competition in the SFRL is shown to be suppressed by the gain saturation effect of the semiconductor optical amplifier. Thus the observed good short-...

It is shown that the interference between amplified spontaneous emission into the nonlasing supermode and the laser field of a semiconductor laser array causes spatial hole burning, which couples the dynamics of the amplified spontaneous emission with the laser field. In particular, phase locking between the amplified spontaneous emission and the lasing mode leads to the formation of a spectral...

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the mo...

For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type ...

This work presents an ultra-low power oscillator designed for wake-up timers in compact wireless sensors. A constant charge subtraction scheme removes continuous comparator delay from the oscillation period, which is the source of temperature dependence in conventional RC relaxation oscillators. This relaxes comparator design constraints, enabling low power operation. In 0.18µm CMOS, the oscill...

We show experimentally that the combination of soft-edged gain and index guiding can lead to resonant excess quantum noise. Resonances with excess noise factors close to 100 are observed in end-pumped Nd3+:YVO4 lasers for cavity lengths in which two modes experience similar gain. An associated increase in the relaxation oscillation damping rate demonstrates that the fluctuation enhancement is i...