Phase synchronization analysis by assessment of the phase difference gradient

2009 ◽  
Vol 19 (2) ◽  
pp. 023120 ◽  
Author(s):  
Martin Vejmelka ◽  
Milan Paluš ◽  
W. T. Lee
Keyword(s):  
Phase Difference ◽  
Phase Synchronization

scholarly journals Intended arm use influences interhemispheric correlation of β-oscillations in primate medial motor areas

2017 ◽  
Vol 118 (5) ◽  
pp. 2865-2883 ◽  
Author(s):  
Toshi Nakajima ◽  
Haruka Arisawa ◽  
Ryosuke Hosaka ◽  
Hajime Mushiake
Keyword(s):  
Phase Difference ◽  
Phase Synchronization ◽  
Ipsilateral Hemisphere ◽  
Β Phase ◽  
Oscillatory Power ◽  
The Right ◽  
Relationship Of ◽  
Selection Of ◽  
Phase Differences

To investigate the role of interhemispheric β-synchronization in the selection of motor effectors, we trained two monkeys to memorize and perform multiple two-movement sequences that included unimanual repetition and bimanual switching. We recorded local field potentials simultaneously in the bilateral supplementary motor area (SMA) and pre-SMA to examine how the β-power in both hemispheres and the interhemispheric relationship of β-oscillations depend on the prepared sequence of arm use. We found a significant ipsilateral enhancement of β-power for bimanual switching trials in the left hemisphere and an enhancement of β-power in the right SMA while preparing for unimanual repetition. Furthermore, interhemispheric synchrony in the SMA was significantly more enhanced while preparing unimanual repetition than while preparing bimanual switching. This enhancement of synchrony was detected in terms of β-phase but not in terms of modulation of β-power. Furthermore, the assessment of the interhemispheric phase difference revealed that the β-oscillation in the hemisphere contralateral to the instructed arm use significantly advanced its phase relative to that in the ipsilateral hemisphere. There was no arm use-dependent shift in phase difference in the pairwise recordings within each hemisphere. Both neurons with and without arm use-selective activity were phase-locked to the β-oscillation. These results imply that the degree of interhemispheric phase synchronization as well as phase differences and oscillatory power in the β-band may contribute to the selection of arm use depending on the behavioral conditions of sequential arm use. NEW & NOTEWORTHY We addressed interhemispheric relationships of β-oscillations during bimanual coordination. While monkeys prepared to initiate movement of the instructed arm, β-oscillations in the contralateral hemisphere showed a phase advance relative to the other hemisphere. Furthermore, the sequence of arm use influenced β-power and the degree of interhemispheric phase synchronization. Thus the dynamics of interhemispheric phases and power in β-oscillations may contribute to the specification of motor effectors in a given behavioral context.

scholarly journals The Phenomenon of Bistable Phase Difference Intervals in the Times-Frequency Vibration Synchronization System Driven by Two Homodromy Exciters

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Lingxuan Li ◽  
Xiaozhe Chen
Keyword(s):  
Phase Difference ◽  
Rotational Speed ◽  
Phase Synchronization ◽  
Perturbation Parameter ◽  
Vibration System ◽  
Synchronization System ◽  
Motion Trajectories ◽  
Frequency Capture ◽  
Perturbation Parameters ◽  
The Times

A vibration system with two homodromy exciters operated in different rotational speed is established to investigate whether the phenomenon of bistable phase difference intervals exists in the times-frequency vibration synchronization system. Some constructive conclusions are proposed. (1) By introducing an average angular velocity perturbation parameter ε0 and two sets of phase difference perturbation parameters and ε2, the frequency capture criterion and the necessary criteria for realizing the times-frequency vibration synchronization are derived. The corresponding stability analysis is carried out. (2) By the theoretical analysis and experiments, it is verified that the times-frequency vibration synchronization system exists the phenomena of bistable phase difference interval. That is, the phase differences between the two homodromy exciters are stable around 180 degrees when they are located at a short distance; the antiphase synchronization phenomenon appears. On the contrary, they are stable around 0 degrees at the in-phase synchronization state. (3) Because of the two homodromy exciters operating in the different rotational speed, the vibration system obtains relatively complex compound motion trajectories; the corresponding application is investigated by adding a feeding material chamber. The times-frequency vibration synchronization system can be used to design the vibration mill for reducing its low-energy zone and developing chaotic mixing equipment for obtaining a better mixing effect.

scholarly journals Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190095 ◽  
Author(s):  
Michael Sebek ◽  
Yoji Kawamura ◽  
Ashley M. Nott ◽  
István Z. Kiss
Keyword(s):  
Phase Difference ◽  
Phase Synchronization ◽  
Single Pair ◽  
Phase Coupling ◽  
Dynamical Interaction ◽  
Phase Dynamics ◽  
Internal Phase ◽  
Phase Models ◽  
External Coupling ◽  
Internal Coupling

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

On Phase and Anti-Phase Combination Synchronization of Time Delay Nonlinear Systems

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Gamal M. Mahmoud ◽  
Ayman A. Arafa ◽  
Emad E. Mahmoud
Keyword(s):  
Time Delay ◽  
Phase Difference ◽  
Phase Synchronization ◽  
Control Technique ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Combination Synchronization ◽  
Phase Combination ◽  
Response Systems ◽  
Control Forces

Extensive studies have been done on the phenomenon of phase and anti-phase synchronization (APS) between one drive and one response systems. As well as, combination synchronization for chaotic and hyperchaotic systems without delay also has been investigated. Thus, this paper aims to introduce the concept of phase and anti-phase combination synchronization (PCS and APCS) between two drive and one response time delay systems, which are not studied in the literature as far as we know. The analysis of PCS and APCS are carried out using active control technique. An example is given to test the validity of the expressions of control forces to achieve the PCS and APCS of time delay systems. This example is between three different systems. When there is no control, the PCS does not occur where the phase difference is unbounded. The bounded phase difference appears when the control is applied which means that PCS is achieved. The special case which is the combination synchronization is studied as well.

scholarly journals Brownian Behavior in Coupled Chaotic Oscillators

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2503
Author(s):  
Francisco Javier Martín-Pasquín ◽  
Alexander N. Pisarchik
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Time Evolution ◽  
Phase Difference ◽  
Stochastic Systems ◽  
Phase Synchronization ◽  
Deterministic Model ◽  
Dynamical Behavior ◽  
Deterministic Models ◽  
Chaotic Oscillators

Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an approach that allows us to analyze chaotic dynamics using the Langevin equation describing dynamics of the phase difference between identical coupled chaotic oscillators. The time evolution of this phase difference can be explained by the biased Brownian motion, which is accepted in quantum mechanics for modeling thermal phenomena. Using a deterministic model based on chaotic Rössler oscillators, we are able to reproduce a similar time evolution for the phase difference. We show how the phenomenon of intermittent phase synchronization can be explained in terms of both stochastic and deterministic models. In addition, the existence of phase multistability in the phase synchronization regime is demonstrated.

scholarly journals Mechanisms of Flexible Information Sharing through Noisy Oscillations

Biology ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 764
Author(s):  
Arthur S. Powanwe ◽  
Andre Longtin
Keyword(s):  
Mutual Information ◽  
Information Sharing ◽  
Phase Difference ◽  
Biological Networks ◽  
Phase Synchronization ◽  
Phase Locking ◽  
Brain Area ◽  
Structural Connectivity ◽  
Field Potential ◽  
Phase Dynamics

Brain areas must be able to interact and share information in a time-varying, dynamic manner on a fast timescale. Such flexibility in information sharing has been linked to the synchronization of rhythm phases between areas. One definition of flexibility is the number of local maxima in the delayed mutual information curve between two connected areas. However, the precise relationship between phase synchronization and information sharing is not clear, nor is the flexibility in the face of the fixed structural connectivity and noise. Here, we consider two coupled oscillatory excitatory-inhibitory networks connected through zero-delay excitatory connections, each of which mimics a rhythmic brain area. We numerically compute phase-locking and delayed mutual information between the phases of excitatory local field potential (LFPs) of the two networks, which measures the shared information and its direction. The flexibility in information sharing is shown to depend on the dynamical origin of oscillations, and its properties in different regimes are found to persist in the presence of asymmetry in the connectivity as well as system heterogeneity. For coupled noise-induced rhythms (quasi-cycles), phase synchronization is robust even in the presence of asymmetry and heterogeneity. However, they do not show flexibility, in contrast to noise-perturbed rhythms (noisy limit cycles), which are shown here to exhibit two local information maxima, i.e., flexibility. For quasi-cycles, phase difference and information measures for the envelope-phase dynamics obtained from previous analytical work using the Stochastic Averaging Method (SAM) are found to be in good qualitative agreement with those obtained from the original dynamics. The relation between phase synchronization and communication patterns is not trivial, particularly in the noisy limit cycle regime. There, complex patterns of information sharing can be observed for a single value of the phase difference. The mechanisms reported here can be extended to I-I networks since their phase synchronizations are similar. Our results set the stage for investigating information sharing between several connected noisy rhythms in neural and other complex biological networks.

scholarly journals Investigation for synchronization of two co-rotating rotors installed with nonlinear springs in a non-resonance system

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983411 ◽  
Author(s):  
Yongjun Hou ◽  
Mingjun Du ◽  
Luyou Wang
Keyword(s):  
Phase Difference ◽  
Phase Synchronization ◽  
Structural Parameters ◽  
Exciting Force ◽  
Resonance System ◽  
Synchronous State ◽  
Vibrating System ◽  
Nonlinear Springs ◽  
Coupling Equations ◽  
Dimensional Coupling

To avoid anti-phase synchronization for two co-rotating rotors system that occurs so that exciting force generated by the vibrating system is very small, a mechanical model of two co-rotating rotors installed with nonlinear springs is proposed to implement synchronization in a non-resonance system. The dynamic equations of the system are first built up by using Lagrange's equation. Second, an analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics of the vibrating system, the non-dimensional coupling equations of two motors are deduced, synchronization problem is converted to that of existence and stability of zero solution for the non-dimensional coupling equations of angular velocity. It is indicated that the synchronous torque of two motors coupled with nonlinear springs in synchronous state must be greater than or equal to the difference of their residual torque. Then, in light of the Routh–Hurwitz criterion, the synchronous criterion of the vibrating system is obtained. Obviously, it is demonstrated that the synchronous state and the stability criterion of the system are influenced by the structural parameters of the coupling unit, coupling coefficients and the positional parameters of two rotors, and so on. Especially, there are clearances in between two nonlinear serial springs, which result in synchronization of the vibrating system that lies in an uncertain state. At last, computer simulations in agreement with the numerical results verify the correctness of the theoretical results for solving the steady phase difference between two rotors. It is demonstrated that adjusting the value of the coupling spring stiffness can make phase difference close to zero to meet the requirements of the strongly exciting force in engineering.

scholarly journals Respiration drives phase synchronization between blood pressure and RR interval following loss of cardiovagal baroreflex during vasovagal syncope

2011 ◽  
Vol 300 (2) ◽  
pp. H527-H540 ◽  
Author(s):  
Anthony J. Ocon ◽  
Marvin S. Medow ◽  
Indu Taneja ◽  
Julian M. Stewart
Keyword(s):  
Blood Pressure ◽  
Phase Difference ◽  
Phase Synchronization ◽  
Vasovagal Syncope ◽  
Hemodynamic Instability ◽  
Subsequent Increase ◽  
Rr Interval ◽  
Control Subjects ◽  
Nonlinear Phase ◽  
End Tidal

Loss of the cardiovagal baroreflex (CVB), thoracic hypovolemia, and hyperpnea contribute to the nonlinear time-dependent hemodynamic instability of vasovagal syncope. We used a nonlinear phase synchronization index (PhSI) to describe the extent of coupling between cardiorespiratory parameters, systolic blood pressure (SBP) or arterial pressure (AP), RR interval (RR), and ventilation, and a directional index (DI) measuring the direction of coupling. We also examined phase differences directly. We hypothesized that AP-RR interval PhSI would be normal during early upright tilt, indicating intact CVB, but would progressively decrease as faint approached and CVB failed. Continuous measurements of AP, RR interval, respiratory plethysomography, and end-tidal CO2 were recorded supine and during 70-degree head-up tilt in 15 control subjects and 15 fainters. Data were evaluated during five distinct times: baseline, early tilt, late tilt, faint, and recovery. During late tilt to faint, fainters exhibited a biphasic change in SBP-RR interval PhSI. Initially in fainters during late tilt, SBP-RR interval PhSI decreased (fainters, from 0.65 ± 0.04 to 0.24 ± 0.03 vs. control subjects, from 0.51 ± 0.03 to 0.48 ± 0.03; P < 0.01) but then increased at the time of faint (fainters = 0.80 ± 0.03 vs. control subjects = 0.42 ± 0.04; P < 0.001) coinciding with a change in phase difference from positive to negative. Starting in late tilt and continuing through faint, fainters exhibited increasing phase coupling between respiration and AP PhSI (fainters = 0.54 ± 0.06 vs. control subjects = 0.27 ± 0.03; P < 0.001) and between respiration and RR interval (fainters = 0.54 ± 0.05 vs. control subjects = 0.37 ± 0.04; P < 0.01). DI indicated respiratory driven AP (fainters = 0.84 ± 0.04 vs. control subjects = 0.39 ± 0.09; P < 0.01) and RR interval (fainters = 0.73 ± 0.10 vs. control subjects = 0.23 ± 0.11; P < 0.001) in fainters. The initial drop in the SBP-RR interval PhSI and directional change of phase difference at late tilt indicates loss of cardiovagal baroreflex. The subsequent increase in SBP-RR interval PhSI is due to a respiratory synchronization and drive on both AP and RR interval. Cardiovagal baroreflex is lost before syncope and supplanted by respiratory reflexes, producing hypotension and bradycardia.

scholarly journals Dynamics of Phase Synchronization between Solar Polar Magnetic Fields Assessed with Van Der Pol and Kuramoto Models

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 945
Author(s):  
Anton Savostianov ◽  
Alexander Shapoval ◽  
Mikhail Shnirman
Keyword(s):  
Time Series ◽  
Magnetic Fields ◽  
Phase Difference ◽  
Coupled Oscillators ◽  
Ad Hoc ◽  
Phase Synchronization ◽  
Solar Dynamo ◽  
The Sun ◽  
Van Der Pol ◽  
Polar Magnetic Fields

We establish the similarity in two model-based reconstructions of the coupling between the polar magnetic fields of the Sun represented by the solar faculae time series. The reconstructions are inferred from the pair of the coupled oscillators modelled with the Van der Pol and Kuramoto equations. They are associated with the substantial simplification of solar dynamo models and, respectively, a simple ad hoc model reproducing the phenomenon of synchronization. While the polar fields are synchronized, both of the reconstruction procedures restore couplings, which attain moderate values and follow each other rather accurately as the functions of time. We also estimate the evolution of the phase difference between the polar fields and claim that they tend to move apart more quickly than approach each other.

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