Phase Synchronization In Systems Research Articles

Matrix equations of the system of phase synchronization

Matrix equations of the system of phase synchronization

A Clock Oscillator Synchronized with a Power Network

A circuit of a clock oscillator is proposed, whose frequency and phase are synchronized with an industrial 50-Hz power network. The synchronization with the network reduces the effect of network-interference impact on signals of low-power sensors during their reproduction, measurement, and processing. The device, which was built using several STTL chips, is a frequency multiplier that is based on a phase-synchronization system with a frequency divider in the feedback loop. Due to the phase–frequency principle of the error-signal formation, the danger of capture at multiple frequencies is eliminated and an extended synchronization band is achieved without parasitic frequency modulation of the generated pulses. The device is powered with a +5-V source and has a synchronization band of ±25% of the rated network frequency. The frequency multiplying factor, which in the described embodiment is 65536 (the clock frequency is 3276.8 kHz), can be set arbitrarily via a conjugate change of the frequency-divider modulus and the oscillator center frequency.

Synthesis of quasi-optimal digital phase-locking systems under the action of additive noises

Quasi-optimal synthesis of digital phase-locking systems (PLSs) is discussed to evaluate the information parameters of a frequency-modulated signal. An adaptive Kalman filter capable of functioning without a priori data on the statistical characteristics of input and test noises is employed. The model of the process under study is identified using the linear trend modified by the self-organization algorithm. Procedures and the results of numerical calculations are presented for the digital system of phase synchronization.

Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis

Groth and Ghil [Phys. Rev. E 84, 036206 (2011)PLEEE81539-375510.1103/PhysRevE.84.036206] developed a modified varimax rotation aimed at enhancing the ability of the multivariate singular spectrum analysis (M-SSA) to characterize phase synchronization in systems of coupled chaotic oscillators. Due to the special structure of the M-SSA eigenvectors, the modification proposed by Groth and Ghil imposes a constraint in the rotation of blocks of components associated with the different subsystems. Accordingly, here we call it a structured varimax rotation (SVR). The SVR was presented as successive pairwise rotations of the eigenvectors. The aim of this paper is threefold. First, we develop a closed matrix formulation for the entire family of structured orthomax rotation criteria, for which the SVR is a special case. Second, this matrix approach is used to enable the use of known singular value algorithms for fast computation, allowing a simultaneous rotation of the M-SSA eigenvectors (a Python code is provided in the Appendix). This could be critical in the characterization of phase synchronization phenomena in large real systems of coupled oscillators. Furthermore, the closed algebraic matrix formulation could be used in theoretical studies of the (modified) M-SSA approach. Third, we illustrate the use of the proposed singular value algorithm for the SVR in the context of the two benchmark examples of Groth and Ghil: the Rössler system in the chaotic (i) phase-coherent and (ii) funnel regimes. Comparison with the results obtained with Kaiser's original (unstructured) varimax rotation (UVR) reveals that both SVR and UVR give the same result for the phase-coherent scenario, but for the more complex behavior (ii) only the SVR improves on the M-SSA.

Frequency-domain criteria for the global stability of phase synchronization systems

New criteria for the global stability of phase synchronization systems are formulated and proved. The efficiency of the criteria for phase-locked loops is demonstrated.

Amplitude and phase noises of a spin-transfer nano-oscillator synchronized by a phase-lock loop

We have studied the amplitude and phase noises of a spin-transfer nano-oscillator (STNO) with a phase synchronization system (phase-lock loop, PLL). Spectral characteristics of the amplitude and phase noises of the isochronous and nonisochronous STNO are obtained and compared to the analogous characteristics of an autonomous (nonsynchronized) oscillator. The PLL bandwidth is determined.

A system of phase synchronization of a spin-transfer nano-oscillator

We have studied the dynamics of a filterless phase-synchronization system (PSS) of a spin-transfer nano-oscillator (STNO) generating microwave oscillations in a broad range of frequencies under the effect of direct current and external magnetic field. Bifurcations in the system caused by a change in the frequency detuning of synchronized oscillations are considered. Bands of phase locking and synchronism are determined. The existence of a phase-locking band in the filterless PSS of STNOs basically distinguishes these oscillators from other types of microwave generators.

Natural Frequency Adaptation as a Mechanism for Phase Synchronization in Neural Systems

AbstractWe consider the problem of adaptive phase synchronization in a system of coupled phase oscillators. The system is limited to a pair of phase oscillators of which the natural frequencies are uncertain, yet they can be tuned. Coupling between the oscillators is allowed to depend on the natural frequencies nonlinearly. Three different mechanisms for the natural frequency self-tuning leading to the emergence of synchronous states are presented and analyzed. The problem is relevant for explaining and modelling phase synchronization and purposeful frequency adaptation in neuronal networks.

A phase synchronization system of two high-speed photographic units (ВФУ-1)

A phase synchronization system of high-speed (up to 4 × 104 frames/s) photographic shooting on two ВФУ-1 units used for studying a vacuum arch is described. The design alterations brought into the ВФУ-1 unit and the designed electronic control circuit allowed one to obtain one- to two-frame phase synchronization and 0.2% rate errors using comparatively simple methods.

Cycle slipping in phase synchronization systems

Cycle slipping is a characteristically nonlinear phenomenon in phase synchronization systems, which is highly dependent of the initial state of the system. Slipping a cycle means that the phase error is increased to such an extent that the generator to be synchronized slips one complete cycle with respect to the input phase. In this Letter, a linear matrix inequality (LMI) based approach is proposed and the estimation of the number of cycles which slips a solution of the system is obtained by solving a quasi-convex optimization problem of LMI. Applications to phase locked loops demonstrate the validity of the proposed approach.

Phase synchronization: Theory and applications

The state-of-the-art of the phase synchronization theory was reviewed. Consideration was given to its applications to the synchronous and induction electrical motors, phase locked loops, and autosynchronization of the unbalanced rotors. The Yakubovich-Kalman frequency theorem was widely used to study the phase synchronization systems for global stability.

On the theory of Thomson self-oscillatory systems

A nonlinear mechanism of the effect of broadband fluctuations on oscillations in a Thomson self-oscillator has been revealed. The correlation function for oscillations, which takes into account all appreciable effects in the second approximation, has been obtained for the first time. A new method has been developed for analyzing steady-state synchronous oscillations in a generator forming a part of the phase-synchronization system; linearized equations of steady-state synchronous oscillations, which take into account the effect of broadband noise, have been developed for the first time. An example of calculation of a complex phase-synchronization system is considered, in which the possibility of synthesizing highly effective systems with the help of the proposed methods of analysis is illustrated. The diffusion coefficients of the phase are estimated.

Onsets, autocorrelation functions and spikes for direction-based sound source separation

The aim of this work is separation of foreground speech from background sound sources using selective remixing of bandpass filtered channels. Clearly, the remixing parameters must be dynamic since the speech and noise spectra are highly non-stationary. Remixing parameters are recomputed at onsets, detected using biologically motivated techniques [L. S. Smith and D. S. Fraser, IEEE TNNS 15, 1125–1134 (2004)]. However, onsets may originate from the foreground or the background. To select appropriate onsets from the foreground source (whose direction is known) a two microphone system is used, selecting onsets for which the estimated direction in that channel corresponds to the foreground direction. Two different techniques for direction estimation are used: a channel by channel short-term autocorrelation technique, and a channel by channel spike based phase synchronous system (SBPSS), computing ITDs [L. S. Smith, in Artificial Neural Networks, Proc ICANN 2001, LNCS 2130, pp. 1103–1108 (Springer, 2001)] and IIDs [L. S. Smith, in From Animals to Animats, Vol. 7, pp. 60–61 (MIT Press, 2002)]. Results comparing the performance of autocorrelation and SBPSS on single source and source plus noise signals in an office environment are presented. [Work supported by UK EPSRC.]

Modeling phase synchronization in systems of two and three coupled oscillators

We determine regions of synchronization of two and three globally coupled oscillators and describe the main mechanisms and bifurcations through which the synchronization of systems is lost.

Architecture of ultrafast optical packet switching ring network

This paper describes the architecture and technical implementation issues of the ultra fast optical packet switching ring network. The technical features of the proposed network are the use of ultrafast optical packets generated by packet compression, ring topology, and out-of-band transmission of the packet control signals. Using present techniques, it is possible to construct a network that is capable of transporting ultrafast optical packets with low delay and guaranteed bandwidth to some packets. Network performance attributes such as scalability, packet delay, and required buffer size are calculated, and implementation issues for realizing optical packet transmission hardware are discussed. Attention is paid to the synchronization in bit/packet phase between packets traversing a ring fiber. A bit/packet phase synchronous system is successfully shown to offer 40 Gb/s, 4000 bit optical packet switching through the use of 2/spl times/2 high-speed electrooptic switches.

Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators.

The transition to phase synchronization in systems consisting of a large number (N) of coupled nonlinear oscillators via the route of phase clustering (phase synchronization among subsets of oscillators) is investigated. We elucidate the mechanism for the merger of phase clusters and find an algebraic scaling between the critical coupling parameter required for phase synchronization and N. Our result implies that, in realistic situations, phase clustering may be more prevalent than full phase synchronization.

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning.

Investigation of a particular mapping of a circle

The one-dimensional mapping of the circle, the mathematical model of a discrete system of phase synchronization, is considered, and certain properties of the Poincaré rotation number and of the sequence of bifurcations which lead to complications in steady motions and to the emergence of stochasticity are established for it.

Stability of pulse-width phase synchronization systems

Stability of pulse-width phase synchronization systems

Qualitative structures and bifurcations generated by a nonlinear third-order phase synchronization equation: PMM vol. 42, no. 5, 1978, pp 808–819

A qualitative investigation is made of a system of nonlinear third-order differential equations, being a model of a phase synchronization system. The existence is established of bifurcation surfaces separating the parameter space into domains for whose points the system is globally asymptotically stable, contains cycles, has a complex structure (contains a denumerable set of saddle cycles), etc.