Clustering behaviors in networks of integrate-and-fire oscillators

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model. © 2008 American Institute of Physics.

Analysis of interconnected oscillators by dissipativity theory

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. © 2007 IEEE.

Dissipativity characterization of a class of oscillators and networks of oscillators

This paper uses dissipativity theory to provide the system-theoretic description of a basic oscillation mechanism. Elementary input-output tools are then used to prove the existence and stability of limit cycles in these "oscillators". The main benefit of the proposed approach is that it is well suited for the analysis and design of interconnections, thus providing a valuable mathematical tool for the study of networks of coupled oscillators.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Observation of locked phase dynamics and enhanced frequency stability in synchronized micromechanical oscillators

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references. © 2013 American Physical Society.

Noise and stability in giant-chirp oscillators mode-locked with a nanotube-based saturable absorber

We compare experimental results showing stable dissipative-soliton solutions exist in mode-locked lasers with ultra-large normal dispersion (as large as 21.5 ps2), with both the analytic framework provided by Haus' master-equation and full numerical simulations. © 2010 Optical Society of America.

Synchronization in a coupled architecture of microelectromechanical oscillators

There has been much recent interest in engineering the phenomenon of synchronization in coupled micro-/nano-scale oscillators for applications ranging from precision time and frequency references to new approaches to information processing. This paper presents descriptive modelling detail and further experimental validation of the phenomenon of mutual synchronization in coupled MEMS oscillators building upon recent experimental validation of this concept by the present authors. In particular, the underlying dependence of the observation of synchronization on system parameters is studied through numerical and analytical modelling while considering essential nonlinearities in both the resonator and circuit domain. Experimental results demonstrating synchronized response are elaborated based on the realization of electrically coupled MEMS resonator based square-wave oscillators. The experimental results on frequency entrainment are found to be in general agreement with results obtained through analytical modeling and numerical simulation. The concept presented here is scalable and could be used to investigate the dynamics of large-arrays of coupled MEMS oscillators. © 2014 AIP Publishing LLC.

Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion

There is much to gain from providing walking machines with passive dynamics, e.g. by including compliant elements in the structure. These elements can offer interesting properties such as self-stabilization, energy efficiency and simplified control. However, there is still no general design strategy for such robots and their controllers. In particular, the calibration of control parameters is often complicated because of the highly nonlinear behavior of the interactions between passive components and the environment. In this article, we propose an approach in which the calibration of a key parameter of a walking controller, namely its intrinsic frequency, is done automatically. The approach uses adaptive frequency oscillators to automatically tune the intrinsic frequency of the oscillators to the resonant frequency of a compliant quadruped robot The tuning goes beyond simple synchronization and the learned frequency stays in the controller when the robot is put to halt. The controller is model free, robust and simple. Results are presented illustrating how the controller can robustly tune itself to the robot, as well as readapt when the mass of the robot is changed. We also provide an analysis of the convergence of the frequency adaptation for a linearized plant, and show how that analysis is useful for determining which type of sensory feedback must be used for stable convergence. This approach is expected to explain some aspects of developmental processes in biological and artificial adaptive systems that "develop" through the embodied system-environment interactions. © 2006 IEEE.

Novel hybrid voltage controlled ring oscillators using single electron and MOS transistors

This paper proposes two kinds of novel hybrid voltage controlled ring oscillators (VCO) using a single electron transistor (SET) and metal-oxide-semiconductor (MOS) transistor. The novel SET/MOS hybrid VCO circuits possess the merits of both the SET circuit and the MOS circuit. The novel VCO circuits have several advantages: wide frequency tuning range, low power dissipation, and large load capability. We use the SPICE compact macro model to describe the SET and simulate the performances of the SET/MOS hybrid VCO circuits by HSPICE simulator. Simulation results demonstrate that the hybrid circuits can operate well as a VCO at room temperature. The oscillation frequency of the VCO circuits could be as high as 1 GHz, with a -71 dBc/Hz phase noise at 1 MHz offset frequency. The power dissipations are lower than 2 uW. We studied the effect of fabrication tolerance, background charge, and operating temperature on the performances of the circuits.

Experimental study on the electric-sweep scanner and ion beam emittance of electron cyclotron resonance ion source

With a latest developed electric-sweep scanner system, we have done a lot of experiments for studying this scanner system and ion beam emittance of electron cyclotron resonance (ECR) ion source. The electric-sweep scanner system was installed on the beam line of Lanzhou electron resonance ion source No. 3 experimental platform of Institute of Modem Physics. The repetition experiments have proven that the system is a relatively dependable and reliable emittance scanner, and its experiment error is about 10%. We have studied the influences of the major parameters of ECR ion source on the extracted ion beam emittance. The typical results of the experiments and the conclusions are presented in this article.