Types Of Oscillators Research Articles

Respiratory pattern generator model using Ca++-induced Ca++ release in neurons shows both pacemaker and reciprocal network properties.

There are two contradictory explanations for central respiratory rhythmogenesis. One suggests that respiratory rhythm emerges from interaction between inspiratory and expiratory neural semicenters that inhibit each other and thereby provide reciprocal rhythmic activity (Brown 1914). The other uses bursting pacemaker activity of individual neurons to produce the rhythm (Feldman and Cleland 1982). Hybrid models have been developed to reconcile these two seemingly conflicting mechanisms (Smith et al. 2000; Rybak et al. 2001). Here we report computer simulations that demonstrate a unified mechanism of the two types of oscillator. In the model, we use the interaction of Ca(++)-dependent K+ channels (Mifflin et al. 1985) with Ca(++)-induced Ca++ release from intracellular stores (McPherson and Campbell 1993), which was recently revealed in neurons (Hernandez-Cruz et al. 1997; Mitra and Slaughter 2002a,b; Scornik et al. 2001). Our computations demonstrate that uncoupled neurons with these intracellular mechanisms show conditional pacemaker properties (Butera et al. 1999) when exposed to steady excitatory inputs. Adding weak inhibitory synapses (based on increased K+ conductivity) between two model neural pools surprisingly synchronizes the activity of both neural pools. As inhibitory synaptic connections between the two pools increase from zero to higher values, the model produces first dissociated pacemaker activity of individual neurons, then periodic synchronous bursts of all neurons (inspiratory and expiratory), and finally reciprocal rhythmic activity of the neural pools.

Q-Deformed and c-Deformed Harmonic Oscillators

Hamilton functions of classical deformed oscillators (c-deformed oscillators) are derived from Hamiltonians of q-deformed oscillators of the Macfarlane and Dubna types. A new scale parameter, lq, with the dimension of length, is introduced to relate a dimensionless parameter characterizing the deformation with the natural length of the harmonic oscillator. Contraction from q-deformed oscillators to c-deformed oscillators is accomplished by keeping lq finite while taking the limit → 0. The c-deformed Hamilton functions for both types of oscillators are found to be invariant under discrete translations: the step of the translation for the Dubna oscillator is half of that for the Macfarlane oscillator. The c-deformed oscillator of the Macfarlane type has propagating solutions in addition to localized ones. Reinvestigation of the q-deformed oscillator carried out in the light of these findings for the c-deformed systems proves that the q-deformed systems are invariant under the same translation symmetries as the c-deformed systems and have propagating waves of the Bloch type.

Noise, Synchronization and Coherence in Chaotic Oscillators

We study effects of noise in two types of chaotic oscillators. The first one, represented by the Rössler system, has very coherent phase dynamics while the amplitude fluctuates strongly. The other type, homoclinic chaos characterized by chaotic spiking behavior, has regular orbits in the phase space while the interspike time intervals vary enormously. We demonstrate that in both classes of systems, noise may play a constructive role to enhance synchronization and generate the most coherent behavior in the collective oscillation of coupled phase coherent oscillators or in the spike sequences of homoclinic chaos.

Whispering-gallery mode splitting in coupled microresonators

Using iterative methods we demonstrate that, for a structure consisting of N-coupled microspheres or ring resonators, the morphology-dependent resonances split into N higher-Q modes, in direct analogy with other types of oscillators. Moreover, for odd numbers of identical lossless coupled rings, the circulating intensity in the innermost ring increases exponentially with N when there is strong coupling to even-numbered rings and weak coupling to odd-numbered rings.

Contribution to the electromechanical and nonlinear properties of GaPO4 crystals.

In the last decade, much attention has been given to piezoelectric crystals with large electromechanical coupling coefficient. The quartz homeotypes berlinite and gallium orthophosphate (GaPO4), along with the calcium gallo-germanates such as langasite are representative of these crystals. The coupling coefficient k26 associated with thickness-shear mode resonators is two times greater than that of quartz, increasing the spacing between the series and parallel resonance frequencies of resonators suitable for the frequency range from 1 to 100 MHz. This is important for some types of crystal oscillators and monolithic filters. The large electromechanical coupling coefficient also increases the difference between the temperature dependencies of the fundamental resonance frequency and its harmonics. In this paper, measured resonance frequency-temperature characteristics of the fundamental and third harmonics of selected rotated Y-cut GaPO4 resonators vibrating in the thickness-shear mode are presented. Further attention is given to the measurement of some nonlinear properties of rotated Y-cut GaPO4 resonators. Knowledge of such nonlinear interactions is important for the analysis of intermodulation phenomena in resonators, and for the application of GaPO4 resonators in crystal oscillators, filters and other electronic devices.

Importance sampling for randomly excited dynamical systems

An importance sampling technique for linear and non-linear dynamical systems subjected to random excitations is presented. Applying a transformation of probability measures, controls are introduced in the system of Itô stochastic differential equations such that the sample trajectories can be influenced in a predetermined way. As is shown, there exist controls resulting in unbiased zero-variance estimators. However, these optimal controls are in general not accessible and have to be replaced by sub-optimal ones derived from an optimization procedure analogous to the first order reliability method known from time-invariant problems. The efficiency of the proposed Monte Carlo simulation technique is demonstrated by estimating first-passage probabilities of typical oscillators under external white-noise excitation.

Photoresponse of self-organizing chemical systems

Research works on the self-organization phenomena in chemical systems are reviewed with particular emphasis on their response to the photo-irradiation, for which most of the works have been performed in the author's laboratory. In the present review, a brief survey is given for the recent developments of research on the self-organization phenomena observed in dark. Then, the determination of action spectra for the photo-irradiated self-organizing chemical systems is described with a few examples, together with a discussion on the advantages of employing the irradiated light intensity as a control parameter. Experimental results for the chemical systems under the stationary and pulse light irradiation are summarized and discussed for the redox oscillators including the Belousov-Zhabotinsky and the Briggs-Rauscher systems and their variations. Discussions are also given for various types of pH oscillators under photo-irradiation. Finally, experimental observations on chaos and multistability, the most characteristic features in the field of self-organizing chemical systems, are surveyed and discussed. Possibility of the photo-control of chaos and multistability is discussed with examples of the Briggs-Rauscher system and of the pH oscillator system, H 2 O 2 - SO 2 - 3 - Fe(CN) 4 - 6 - HCO - 3 .

The correlation time of mesoscopic chemical clocks

A formula is proved for the correlation time of nonequilibrium chemical clocks in the presence of molecular noise. The correlation time is defined as the inverse of the damping rate of the autocorrelation functions of the chemical concentrations. Using the Hamilton–Jacobi method for stochastic systems as well as a Legendre transform from the Onsager–Machlup action to a reduced action depending only on the Hamilton–Jacobi pseudoenergy, the correlation time is given in the weak-noise limit in terms of the extensivity parameter, the period of oscillations, as well as the derivative of the period with respect to the pseudoenergy. Using this result, an estimation is obtained for the minimum number of molecules required for the oscillations of the chemical concentrations to remain correlated in time. This estimation puts a fundamental lower limit on the size of chemical clocks. For typical oscillators, the minimum number of molecules is estimated between ten and one hundred, which essentially corresponds to nanometric systems.

Braided oscillators

A generalized oscillator algebra is proposed and the braided Hopf algebra structure for this generalized oscillator is investigated. Using the solutions for the braided Hopf algebra structure, two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn–Macfarlane oscillators as special cases of the Fibonacci oscillators. We also find the braided Hopf algebra solutions for the three dimensional braided space. One of these, as a special case, gives the Hopf algebra given in the literature.

System Size Resonance in Coupled Noisy Systems and in the Ising Model

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles---lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.

Comparative study of alternative circuit configurations for inductive sensors

We study three different electronic circuit configurations for the excitation, recovering and analysis of the response of magnetic sensors based on inductive changes. The best characteristics are sought: maximum output, stability, linearity and large sensibility together with an economic design. To simulate the sensible element, we use a general coil with mobile magnetic core that resembles any real case where variations of induction take place. Three parts are readily distinguished in the circuits: oscillator, filter and rectifier. In one of the tested configurations the variable inductance is part of the oscillator, whereas in the other two, it is used in the filter. In turn, two different types of common oscillators are investigated: Colpitts and Wien bridge. The best option turns out to be the one composed by a Wien bridge oscillator with the variable inductance in the filter.

The total deviation approach to long-term characterization of frequency stability

Total variance represents the first advancement in the estimation of an oscillating signal's long-term frequency stability since the conventional Allan variance estimator. It is called "Totvar" (pronounced tot-var) for short. Its commonly reported square-root is the total deviation function called "Totdev" (tot-dev). Totdev efficiently extracts broadband FM oscillator noise levels and types commonly encountered at long-term tau-averaging times, even though these are difficult to measure. The notable advantages of Totdev include: significantly improved confidence for estimating long-term frequency stability, lower sensitivity to the removal of linear frequency drift, and exact decomposition of the sample variance of frequency residuals. A review of some methods of improving the estimation of long-term stability is presented. Concepts of data extrapolation and smoothing are developed and linked to the definition of Totdev. The approach to interpreting a sigma vs. tau stability plot of Totdev is given and is identical to that using the Allan deviation. Formulas are given for computing confidence interval at long term and for computing an easily removed, slight negative bias. The last section shows how Totdev is the first frequency-stability statistic that is unified to the more readily understood, but often inappropriate, standard deviation by an exact decomposition.

From metaphors to equations: How can we find the good ones?

Among the metaphors used in the target article are “musical instruments,” “water waves,” and other types of mechanical oscillators. The corresponding equations have inertial properties and lead to standing waves that depend on boundary conditions. Other, physiologically relevant quantities like refractory times are not contained in the mechanical oscillator model but occur naturally, for instance, in biological forest fire metaphors.

Communicating with noise: How chaos and noise combine to generate secure encryption keys.

An approach for the secure transmission of encrypted messages using chaos and noise is presented in this paper. The method is based on the synchronization of certain types of chaotic oscillators in response to a common noise input. This allows two distant oscillators to generate identical output which can be used as a key for encryption and decryption of a message signal. The noiselike synchronizing input-which contains no message information-is communicated to identical oscillators in the transmitter and the receiver over a public channel. The encrypted message is also sent over a public channel, while the key is never transmitted at all. The chaotic nature of the oscillators which generate the key and the randomness of the signal driving the process combine to make the recovery of the key by an eavesdropper extremely difficult. We evaluate system performance with respect to security and robustness and show that a robust and secure system can be obtained. (c) 1998 American Institute of Physics.

Decay ratio for third order brownian oscillators

We have obtained the analytical expressions of the decay ratios for two types of third order Brownian oscillators which are generalizations of the second order Brownian oscillator driven by the Gaussian-white noise. The resulting expressions will provide us useful baseline information for more complicated practical problems and their applications.

Modeling of tunnel diode oscillators and their use for some low temperature investigations

The simple method of modeling of tunnel diode (TD) oscillators’ work is described, and may be applied also to the other types of negative-differential conductance oscillators. In particular, the calculation of the harmonic oscillation amplitude is performed by the energy balance method, based on TD measured the current–voltage characteristic’ (I–V curve), using only one fitting parameter—the tunnel diode’s measured bias at which oscillations are quenched by means of which the oscillator’s effective total losses are determined also. The formula for calculation of the TD generator’s frequency is derived; it agrees with experiment and permits determination of its dependence on the radiotechnical scheme’s elements and TD I–V curve’s shape. The results of the calculation in comparison with the experiment are reported for the oscillators of various constructions operating at different conditions. For this, more attention is given to the constructive solutions applied in the low temperature experiments. Examples of the TD oscillators’ use in cryogenic techniques as well as in the superconducting detectors of particles and radiation are presented. The oscillators described generate, under the certain conditions, low-amplitude (<40 mV) sinusoidal signals with a highly stable frequency (not worse than ΔF/F=10−9/min at liquid-helium temperatures) and low intensity of higher harmonics in the soft mode. The power released is less than 10 μW and the measuring rf magnetic field’s amplitude at a sample, placed inside or near the oscillator coil, is less than 1 mOe. Using designed facilities we have already detected normal-to-superconducting phase transitions of tin grains with diameters of about 2 μm and phase transitions in micrometer thick and 20 μm2 high-Tc superconducting films.

Volume delivery during high frequency oscillation

AIMTo examine the delivered volume during “high volume strategy” high frequency oscillation, used as rescue treatment in preterm infants; and to identify factors, other than frequency and oscillatory amplitude, influencing...

A general theory of phase noise in electrical oscillators

A general model is introduced which is capable of making accurate, quantitative predictions about the phase noise of different types of electrical oscillators by acknowledging the true periodically time-varying nature of all oscillators. This new approach also elucidates several previously unknown design criteria for reducing close-in phase noise by identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total phase noise. In particular, it explains the details of how 1/f noise in a device upconverts into close-in phase noise and identifies methods to suppress this upconversion. The theory also naturally accommodates cyclostationary noise sources, leading to additional important design insights. The model reduces to previously available phase noise models as special cases. Excellent agreement among theory, simulations, and measurements is observed.

Electrode type membrane diffusion oscillator

PERIODIC and chaotic phenomena in the living system are closely related with the diffusion process through a membrane. In order to understand the relation, the exploration has been carried out continuously. So far, several types of membrane oscillators have been found, such as solid membrane oscillator, liquid membrane oscillator and salt-water oscillator. But the relationships between these various oscillators and experimental conditions of the transition from oscillation...

Josephson array oscillators with microstrip resonators

Interaction between two Josephson junctions and a microstrip resonator is investigated using a resonator shunted junction (RLCSJ) model. A sharp current step resulting from coupling with the resonator is observed in simulated I-V characteristics. There is strong phase-locking and decreasing of dynamic resistance at the current step. We design and fabricate two types of Josephson array oscillators using these effects to obtain stable phase locking and narrow linewidth for the oscillation. The fabricated oscillators are formed with nine shunted Nb/AlOx/Nb tunnel junctions and Nb microstrip resonators. The power of the oscillator delivered to the load resistor was estimated to be about 3.6 /spl mu/W at 330 GHz. A composite linewidth of the oscillators is also measured at about 19 MHz at 4.2 K using two oscillators with a log-periodic antenna and a SIS detector.