Phase-locked Oscillator Research Articles

Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators

In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω, that might correspond to Hopf bifurcations in each case for critical values of the delay. The Sn map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.

Neural basis of postural focus effect on concurrent postural and motor tasks: Phase-locked electroencephalogram responses

Dual-task performance is strongly affected by the direction of attentional focus. This study investigated neural control of a postural–suprapostural procedure when postural focus strategy varied. Twelve adults concurrently conducted force-matching and maintained stabilometer stance with visual feedback on ankle movement (visual internal focus, VIF) and on stabilometer movement (visual external focus, VEF). Force-matching error, dynamics of ankle and stabilometer movements, and event-related potentials (ERPs) were registered. Postural control with VEF caused superior force-matching performance, more complex ankle movement, and stronger kinematic coupling between the ankle and stabilometer movements than postural control with VIF. The postural focus strategy also altered ERP temporal-spatial patterns. Postural control with VEF resulted in later N1 with less negativity around the bilateral fronto-central and contralateral sensorimotor areas, earlier P2 deflection with more positivity around the bilateral fronto-central and ipsilateral temporal areas, and late movement-related potential commencing in the left frontal-central area, as compared with postural control with VIF. The time–frequency distribution of the ERP principal component revealed phase-locked neural oscillations in the delta (1–4Hz), theta (4–7Hz), and beta (13–35Hz) rhythms. The delta and theta rhythms were more pronounced prior to the timing of P2 positive deflection, and beta rebound was greater after the completion of force-matching in VEF condition than VIF condition. This study is the first to reveal the neural correlation of postural focusing effect on a postural–suprapostural task. Postural control with VEF takes advantage of efficient task-switching to facilitate autonomous postural response, in agreement with the “constrained-action” hypothesis.

Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits.

The parametric phase-locked oscillator (PPLO) is a class of frequency-conversion device, originally based on a nonlinear element such as a ferrite ring, that served as a fundamental logic element for digital computers more than 50 years ago. Although it has long since been overtaken by the transistor, there have been numerous efforts more recently to realize PPLOs in different physical systems such as optical photons, trapped atoms, and electromechanical resonators. This renewed interest is based not only on the fundamental physics of nonlinear systems, but also on the realization of new, high-performance computing devices with unprecedented capabilities. Here we realize a PPLO with Josephson-junction circuitry and operate it as a sensitive phase detector. Using a PPLO, we demonstrate the demodulation of a weak binary phase-shift keying microwave signal of the order of a femtowatt. We apply PPLO to dispersive readout of a superconducting qubit, and achieved high-fidelity, single-shot and non-destructive readout with Rabi-oscillation contrast exceeding 90%.

Chimera Type Behavior in Nonlocal Coupling System with Two Different Inherent Frequencies

From the research of Kuramoto and Strogatz, arrays of identical oscillators can display a remarkable pattern, named chimera state, in which phase-locked oscillators coexist with drifting ones in nonlocal coupling oscillator system. We consider further in this study, two groups of oscillators with different inherent frequencies and arrange them in a ring. When the difference of the inherent frequencies is within some specific parameter range, oscillators of nonlocal coupling system show two distinct chimera states. When the parameter value exceeds some threshold value, two chimera states disappear. They show different features. The statistical dynamic behavior of the system can be described by Kuramoto theory.

Mutual Pulling Between Two Oscillators

Behavior of two mutually coupled phase-locked or free-running oscillators with nearby frequencies is studied. In the case of two free-running mutually coupled oscillators, the two oscillators are either locked to a common frequency, or they undergo through a mutual pulling interaction. It is shown that center frequencies of the pulled oscillators come closer, however, they do not necessarily approach toward each other from opposite directions. It is also demonstrated that the strengths of mutual injections as well as the phase-shifts experienced by the mutually injected signals, affect locations of the two center frequencies. The paper also studies impacts of phase-locked loops on the location and magnitude of the sidebands, when the two mutually coupled oscillators are phase-locked. Effects of the phase-shifts endured by the mutually injected signals on the sidebands are also discussed.

Extensive Oscillatory Gene Expression during C. elegans Larval Development

Oscillations are a key to achieving dynamic behavior and thus occur in biological systems as diverse as the beating heart, defecating worms, and nascent somites. Here we report pervasive, large-amplitude, and phase-locked oscillations of gene expression in developing C. elegans larvae, caused by periodic transcription. Nearly one fifth of detectably expressed transcripts oscillate with an 8 hr period, and hundreds change >10-fold. Oscillations are important for molting but occur in all phases, implying additional functions. Ribosome profiling reveals that periodic mRNA accumulation causes rhythmic translation, potentially facilitating transient protein accumulation as well as coordinated production of stable, complex structures such as the cuticle. Finally, large-amplitude oscillations in RNA sampled from whole worms indicate robust synchronization of gene expression programs across cells and tissues, suggesting that these oscillations will be a powerful new model to study coordinated gene expression in an animal.

Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators

To elucidate how a biological rhythm is regulated, the extended (three-dimensional) Bonhoeffer-van der Pol or FitzHugh-Nagumo equations are employed to investigate the dynamics of a population of neuronal oscillators globally coupled through a common buffer (mean field). Interesting phenomena, such as extraordinarily slow phase-locked oscillations (compared to the natural period of each neuronal oscillator) and the death of all oscillations, are observed. We demonstrate that the slow synchronization is due mainly to the existence of "fast" oscillators. Additionally, we examine the effect of noise on the synchronization and variability of the interspike intervals. Peculiar phenomena, such as noise-induced acceleration and deceleration, are observed. The results herein suggest that very small noise may significantly influence a biological rhythm.

Multiple bifurcation analysis in a ring of delay coupled oscillators with neutral feedback

Spatiotemporal periodic patterns, including phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or anti-phase oscillations are investigated in a ring of bidirectionally coupled oscillators with neutral delay feedback. It is confirmed that neutral feedback makes Hopf bifurcation occur in a larger domain of parameters. We calculate the normal forms near Hopf bifurcation, D N equivariant Hopf bifurcation and double-Hopf bifurcation in this neutral equation by using the method of multiple scales. Theoretically, the appearance of the in-phase, anti-phase and phase-locked oscillations that we observed in the simulation about a ring of delay coupled Hindmarsh–Rose neurons with neutral feedback is explained.

Phase-locked magnetoconductance oscillations as a probe of Majorana edge states

We calculate the Andreev conductance of a superconducting ring interrupted by a flux-biased Josephson junction, searching for electrical signatures of circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes and (chiral or helical) Majorana modes. These produce h/e-periodic magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured via an N-mode point contact at the inner or outer perimeter of the grounded ring. For Dirac modes the oscillations in the two contacts are independent, while for an unpaired Majorana mode they are phase locked by a topological phase transition at the Josephson junction.

Phase- and Self-Injection-Locked Radar for Detecting Vital Signs with Efficient Elimination of DC Offsets and Null Points

A phase- and self-injection-locked radar is presented for robust vital-sign detection. The dc offset from the clutter is eliminated by using a dual-tuning voltage-controlled oscillator without complex clutter cancellation techniques. Phase noise analysis shows that the proposed radar has the advantages of both phase-locked oscillators and self-injection-locked oscillators to achieve high power spectral signal-to-noise ratio. Path-diversity transmission is employed to eliminate null points and reduce average transmitted power. Experiments demonstrate successful detection of breathing and heartbeat from a distance of 4 m with -22 dBm (6 μW ) average transmitted power.

A Two Sweeping VCO Source for Heterodyne FMCW Radar

We propose and develop a heterodyne frequency modulated continuous wave (FMCW) radar system. The system operates at 14 GHz with a 500-MHz bandwidth in a 100-μs sweeping period, based on two wideband linear RF voltage-controlled oscillator (VCO) sweeping sources, which are controlled by a direct digital synthesizer (DDS) through a phase-locked scheme, leading to a high linearity of the frequency chirping signal. To achieve low phase noise, the RF signals are synthesized from low-noise baseband signals which are generated through a generation scheme of using phase-locked oscillators operating in the 800-MHz frequency range. Additionally, the proposed architecture can eliminate the phase noise contributions and/or frequency deviation due to the uncorrelation of different VCOs. The results are verified through measurements and derivation.

Excitation of parasitic waves in forward-wave amplifiers with weak guiding fields

To produce high-power coherent electromagnetic radiation at frequencies from microwaves up to terahertz, the radiation sources should have interaction circuits of large cross sections, i.e., the sources should operate in high-order modes. In such devices, the excitation of higher-order parasitic modes near cutoff where the group velocity is small and, hence, start currents are low can be a serious problem. The problem is especially severe in the sources of coherent, phase-controlled radiation, i.e., the amplifiers or phase-locked oscillators. This problem was studied earlier [Nusinovich, Sinitsyn, and Antonsen, Phys. Rev. E 82, 046404 (2010)] for the case of electron focusing by strong guiding magnetic fields. For many applications it is desirable to minimize these focusing fields. Therefore in this paper we analyze the problem of excitation of parasitic modes near cutoff in forward-wave amplifiers with weak focusing fields. First, we study the large-signal operation of such a device with a signal wave only. Then, we analyze the self-excitation conditions of parasitic waves near cutoff in the presence of the signal wave. It is shown that the main effect is the suppression of the parasitic wave in large-signal regimes. At the same time, there is a region of device parameters where the presence of signal waves can enhance excitation of parasitic modes. The role of focusing fields in such effects is studied.

Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations

The minimal integrate-and-fire-or-burst neuron model succinctly describes both tonic firing and postinhibitory rebound bursting of thalamocortical cells in the sensory relay. Networks of integrate-and-fire-or-burst (IFB) neurons with slow inhibitory synaptic interactions have been shown to support stable rhythmic states, including globally synchronous and cluster oscillations, in which network-mediated inhibition cyclically generates bursting in coherent subgroups of neurons. In this paper, we introduce a reduced IFB neuronal population model to study synchronization of inhibition-mediated oscillatory bursting states to periodic excitatory input. Using numeric methods, we demonstrate the existence and stability of 1:1 phase-locked bursting oscillations in the sinusoidally forced IFB neuronal population model. Phase locking is shown to arise when periodic excitation is sufficient to pace the onset of bursting in an IFB cluster without counteracting the inhibitory interactions necessary for burst generation. Phase-locked bursting states are thus found to destabilize when periodic excitation increases in strength or frequency. Further study of the IFB neuronal population model with pulse-like periodic excitatory input illustrates that this synchronization mechanism generalizes to a broad range of n:m phase-locked bursting states across both globally synchronous and clustered oscillatory regimes.

Multiple scales and normal forms in a ring of delay coupled oscillators with application to chaotic Hindmarsh–Rose neurons

We study the appearance and stability of spatiotemporal periodic patterns like phase-locked oscillations, mirror-reflecting waves, standing waves, in-phase or antiphase oscillations, and coexistence of multiple patterns, in a ring of bidirectionally delay coupled oscillators. Hopf bifurcation, Hopf–Hopf bifurcation, and the equivariant Hopf bifurcation are studied in the viewpoint of normal forms obtained by using the method of multiple scales which is a kind of perturbation technique, thus a clear bifurcation scenario is depicted. We find time delay significantly affects the dynamics and induces rich spatiotemporal patterns. With the help of the unfolding system near Hopf–Hopf bifurcation, it is confirmed in some regions two kinds of stable oscillations may coexist. These phenomena are shown for the delay coupled limit cycle oscillators as well as for the delay coupled chaotic Hindmarsh–Rose neurons.

Resonant Tunneling Diode Optoelectronic Circuits Applications in Radio-Over-Fiber Networks

Phase-locked oscillators based on resonant tunneling diodes are used in this study to implement transceiver components that perform conversion between optical and wireless phase shift-keyed signals using injection-locked oscillator techniques. Three different links are demonstrated at frequencies of 940 MHz, 1.3 GHz, and 3.2 GHz that are capable of locking to a phase-modulated signal that propagates from the optical to the wireless and back to the optical domains. The transmitter and receiver are evaluated through Gaussian minimum shift-keying modulation accuracy metrics. Deployment of the transceiver in radio-over-fiber architectures is also discussed.

A method for controlling the phase locking of a multichannel laser system

The conditions leading to control over phase-locked oscillation in a set of three loop lasers containing self-pumped phase-conjugate gain-grating mirrors by using a LiF: F2− passive Q-switch are studied both experimentally and theoretically. Cases of spatially uniform lamp pumping and high-efficiency spatially nonuniform transverse diode pumping are considered.

Spike-Timing Precision and Neuronal Synchrony Are Enhanced by an Interaction between Synaptic Inhibition and Membrane Oscillations in the Amygdala

The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (∼2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ∼300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ∼130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.

A processing scheme for time-variant phase analysis in EEG burst activity of premature and full-term newborns in quiet sleep: a methodological study

A processing scheme for the investigation of neonatal electroencephalographic burst oscillations that is composed of time-variant methods for linear and nonlinear phase analysis is introduced. Starting from a time-frequency analysis of oscillations' amplitudes, time-variant approaches for quantification of phase locking, n:m phase synchronization, and quadratic phase coupling are applied. Tracé discontinue patterns from premature newborns and tracé alternant patterns from full-term newborns were investigated using bipolar EEG recordings. Maturation-related differences between the burst generation mechanisms can be shown, which are reflected in group-specific patterns of augmentation, timing, and grouping of time-varying phase characteristics of the EEG burst oscillations. We demonstrate for both groups (premature and full-term newborns) that phase-locked low-frequency oscillations are pronounced in the frequency range of 0.5-1.5 Hz. Phase-locked oscillations also occur in a frequency range of >3 Hz. The amplitude of a phase-locked 2-Hz oscillation is higher in full-term than in premature newborns. After onset, n:m synchronization and an increase in bicoherence occur earlier in the premature group (between 0.5-1.5 Hz and 3.0-6.0 Hz). It can be suggested that during the maturation process, the driving force of thalamic structures decreases and that cortical activity plays an increasingly important role in the process of burst generation.

Specifying Upper Bounds on the Phase Noise in Phase-Locked Oscillators in Electronic Warfare Systems—Part II [Application Notes

This continuation of my previous application note presents the general mechanism that causes common-mode coupling in mixers. Common mode coupling can increase the noise figure in receivers and/or transmitters. Also presented is a method of calculating the effect of vibration on phase noise in phase-locked oscillators (PLOs). When combined with the techniques presented in Part I, these methods allow an engineer to determine an upper bound on phase noise, and will help engineers decide which PLO is the best for his or her application.

Neural Oscillations Carry Speech Rhythm through to Comprehension.

A key feature of speech is the quasi-regular rhythmic information contained in its slow amplitude modulations. In this article we review the information conveyed by speech rhythm, and the role of ongoing brain oscillations in listeners’ processing of this content. Our starting point is the fact that speech is inherently temporal, and that rhythmic information conveyed by the amplitude envelope contains important markers for place and manner of articulation, segmental information, and speech rate. Behavioral studies demonstrate that amplitude envelope information is relied upon by listeners and plays a key role in speech intelligibility. Extending behavioral findings, data from neuroimaging – particularly electroencephalography (EEG) and magnetoencephalography (MEG) – point to phase locking by ongoing cortical oscillations to low-frequency information (~4–8 Hz) in the speech envelope. This phase modulation effectively encodes a prediction of when important events (such as stressed syllables) are likely to occur, and acts to increase sensitivity to these relevant acoustic cues. We suggest a framework through which such neural entrainment to speech rhythm can explain effects of speech rate on word and segment perception (i.e., that the perception of phonemes and words in connected speech is influenced by preceding speech rate). Neuroanatomically, acoustic amplitude modulations are processed largely bilaterally in auditory cortex, with intelligible speech resulting in differential recruitment of left-hemisphere regions. Notable among these is lateral anterior temporal cortex, which we propose functions in a domain-general fashion to support ongoing memory and integration of meaningful input. Together, the reviewed evidence suggests that low-frequency oscillations in the acoustic speech signal form the foundation of a rhythmic hierarchy supporting spoken language, mirrored by phase-locked oscillations in the human brain.