The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical pro...

The behavior of arrays of coupled oscillators has been previously studied by computational solution of a set of nonlinear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators. The equations are sufficiently complicated in that intuitive understanding of the phenomena which arise is exceedingly difficult. We prop...

Voltage-controlled oscillators are widely used circuit blocks, particularly in phase-locked loops. As CMOS is the technology of choice for many applications, CMOS oscillators with low phase noise and timing jitter are highly desired. CMOS ring oscillators with five different delay cell topologies have been designed, fabricated and evaluated for phase noise performance. Our results show that rin...

We derive conditions for the existence of traveling wave solutions in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbor interactions and distributed delays. A linear stability analysis of the traveling waves is carried out in terms of perturbations of the firing times of the oscillators. It is shown how traveling waves destabilize when the detuning between oscillator...

We develop performance criteria for the objective comparison of different classes of singledegree-of-freedom oscillators under stochastic excitation. For each family of oscillators, these objective criteria take into account the maximum possible energy harvested for a given response level, which is a quantity that is directly connected to the size of the harvesting configuration. We prove that ...

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator as a figure of merit for its amplitude stability. It can be formulated rigorously and computed numerically from oscillator equations. With this definition, w...

In this paper, we study the behavior of pulsecoupled integrate-and-fire oscillators. Each oscillator is characterized by a state evolving between two threshold values. As the state reaches the upper threshold, it is reset to the lower threshold and emits a pulse which increments by a constant value the state of every other oscillator. The behavior of the system is described by the so-called fir...

In this paper, we propose the first numerical study of nanotube-based torsional oscillators via developing a new multiscale model. The edge-to-edge technique was employed in this multiscale method to couple the molecular model, i.e., nanotubes, and the continuum model, i.e., the metal paddle. Without losing accuracy, the metal paddle was treated as the rigid body in the continuum model. Torsion...