Phase Oscillators Research Articles

Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data

Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data

Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise.

We report the effect of nonlinear bias of the frequency of collective oscillations of sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes the Ott-Antonsen ansatz inapplicable. We argue that, for all stable non-Gaussian noises, the tail asymmetry is not only possible (in addition to the trivial shift of the distribution median) but also generic in many physical and biophysical setups. For the theoretical description of the effect, we develop a mathematical formalism based on the circular cumulants. The derivation of rigorous asymptotic results can be performed on this basis but seems infeasible in traditional terms of the circular moments (the Kuramoto-Daido order parameters). The effect of the entrainment of individual oscillator frequencies by the global oscillations is also reported in detail. The accuracy of theoretical results based on the low-dimensional circular cumulant reductions is validated with the high-accuracy "exact" solutions calculated with the continued fraction method.

Particle production and density fluctuations of nonclassical inflaton in coherent squeezed vacuum state of flat FRW universe

In this paper, we study nonclassical inflaton, which is minimally coupled to the semi-classical gravity in FRW universe in Coherent Squeezed Vacuum State (CSVS). We have determined the Oscillatory phase of inflaton, power-law expansion, scale factor, density fluctuations, quantum fluctuations and particle production for CSVS. We have obtained an estimated leading solution of scale factor in CSVS and found it proportional to [Formula: see text] and showing similar diversification as demonstrated by Semi-classical Einstein Equation (SCEE) of gravity in matter dominated universe. We have also studied the validity of SCEE in CSVS. We have computed validity of uncertainty relation for FRW Universe by determining the quantum fluctuation for CSVS. Our results show that Quantum fluctuations don’t depend on coherent parameter [Formula: see text] as the uncertainty relation doesn’t effect by the displacement of [Formula: see text] in phase space. We have also studied the production of particles in CSVS for oscillating massive inflaton in flat FRW universe.

Leveraging Data From Defunct Gillnet Fisheries to Understand the Distributional Dynamics of a Rare Pelagic Fish, the Louvar (Luvarus imperialis)

ABSTRACTThe louvar (Luvarus imperialis) is an exceedingly rare circumtropical fish species with a poorly understood ecology. Catch data from defunct drift gillnet fisheries provide an unparalleled way to quantify the distributional dynamics of this species that, as a gelativore, is almost never taken as bycatch on fish‐ or squid‐baited longlines that dominate modern open ocean fisheries. Here, we present the largest observational dataset assembled for louvar, combining > 30 years of observer presence–absence records from two such fisheries spanning a vast expanse of the pelagic North Pacific. We leverage these data to construct a species distribution model that quantifies the species' environmental preferences, enabling us to confront the knowledge gaps on its core distribution and investigate variability among seasons, years, and alternate phases of climate oscillations. We show that this enigmatic species favors waters with positive sea surface height and shallow mixed layer depth, consistent with high, but seasonally variable, model‐predicted suitable habitat in the North Pacific Transition Zone and California Current. In addition, our results suggest that louvar have experienced slight loss of habitat from 1990 to 2023 in response to large‐scale climate oscillations. This study highlights the value of using a species distribution model framework to synthesize diverse datasets, characterize species–environment relationships, and infer basic spatiotemporal dynamics for rare species that cannot be reliably sampled.

The Combined and Isolated Impacts of El Niño and Positive Indian Ocean Dipole Events on South American Precipitation During Austral Winter and Spring Depending on the Atlantic Multidecadal Oscillation Phases

ABSTRACTThe isolated/combined impacts of the positive Indian Ocean Dipole (pIOD) and El Niño (EN) events on precipitation in South America (SA) were investigated during austral winter and spring for the 1901–2012 period, considering both Atlantic Multidecadal Oscillation (AMO) phases. Under the warm phase (WAMO), EN events are well characterised in winter and, in spring, are accompanied by anomalous warming of the Tropical North Atlantic (TNA); thus, variations in the Walker circulation and the northward shifted Intertropical Convergence Zone (ITCZ) reduce precipitation over northern SA. In the cold AMO phase (CAMO), EN events are weak in winter. At the same time, an intense cooling in the equatorial North Atlantic, favoured by the CAMO, enhances moisture transport from the Amazon to central and southeastern Brazil, increasing precipitation in the South Atlantic Convergence Zone region. As EN develops in spring, the anticyclone off the east coast of SA associated with the Pacific‐South American (PSA) pattern decreases (increases) precipitation in central (southeastern) SA. The pIOD events predominantly occur during WAMO phase, when warming in the TNA is favoured by AMO. In winter, the moisture transport to northern SA is weakened, and the ITCZ remains northward shifted, inhibiting the precipitation over northeastern Brazil and southeastern Amazon. In spring, pIOD intensified ascending motions in equatorial Atlantic, increasing precipitation over northeastern Brazil. A wave train from the Indian Ocean strengthens the South Atlantic subtropical high, suppressing precipitation in central and eastern SA. EN‐pIOD events are well established in both AMO phases, though the sea surface temperature anomalies in the TNA depend on the AMO. During WAMO, reduced precipitation in western Amazon and northeastern SA is influenced by the Walker circulation, while in CAMO, TNA cooling enhances moisture transport from the Amazon into southeastern SA, where the PSA pattern and wave train from the Indian Ocean increase precipitation.

Unforced Millennial-Scale Oscillations in a Coupled Climate-Carbon System

Abstract We identify and investigate spontaneous unforced millennial-scale oscillations in an idealized global coupled climate-carbon model under nearly ice-free conditions. The oscillations first appear due to gradual loss of deep polar ocean stratification in a global warming scenario, which triggers the onset of a subpolar deep circulation, with important implications for ocean carbon storage. Analysis focuses on the residual mean Meridional Overturning Circulation (MOC) due to the significant eddy-driven component. The subpolar deepMOCfurther invigorates the subtropical deep MOC, increasing global air-sea CO2 fluxes and atmospheric CO2 through upwelling of deep Dissolved Inorganic Carbon (DIC). The increasing atmospheric CO2 leads to global surface warming that further warms and stratifies the subsurface polar ocean, shutting down the subpolar deep MOC and completing a delayed negative feedback which reverses the oscillation phase. Mechanism-denial experiments reveal that CO2 radiative feedback and time-varying MOC and polar stratification are all essential components of the oscillator mechanism, while winter sea ice and time-varying biological nutrients are not. The millennial timescale is determined by the delayed response of atmospheric CO2 to variations in polar stratification and subpolar deep MOC. This study sheds light on the coupled carbon-climate dynamics behind the internal millennial-scale variability of an ice-free warm climate. We discuss the relevance to understanding observed millennial-scale climate variability during the last glacial period.

Local Predictors of Explosive Synchronization with Ordinal Methods

We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early warning signal (EWS) measures and could be valuable to the tools available for predicting critical transitions. In particular, we investigate networks of diffusively coupled phase oscillators and chaotic Rössler systems. As maps, we consider a neural network of Chialvo maps coupled in star and scale-free configurations. Furthermore, we apply this measure to time series data obtained from a network of electronic circuits operating in the chaotic regime.

Decomposition of skill scores for conditional verification: impact of Atlantic Multidecadal Oscillation phases on the predictability of decadal temperature forecasts

Abstract. As the performance of weather and climate forecasting systems and their benchmark systems are generally not homogeneous in time and space and may vary in specific situations, improvements in certain situations or subsets have different effects on overall skill. We present a decomposition of skill scores for the conditional verification of such systems. The aim is to evaluate the performance of a system individually for predefined subsets with respect to the overall performance. The overall skill score is decomposed into a weighted sum representing subset contributions, where each individual contribution is the product of the following: (1) the subset skill score, assessing the performance of a forecast system compared to a reference system for a particular subset; (2) the frequency weighting, accounting for varying subset size; and (3) the reference weighting, relating the performance of the reference system in the individual subsets to the performance of the full data set. The decomposition and its interpretation are exemplified using synthetic data. Subsequently, we use it for a practical example from the field of decadal climate prediction: an evaluation of the Atlantic European near-surface temperature forecast from the German “Mittelfristige Klimaprognosen” (MiKlip) initiative decadal prediction system that is conditional on different Atlantic Multidecadal Oscillation (AMO) phases during initialization. With respect to the chosen western European North Atlantic sector, the decadal prediction system “preop-dcpp-HR” performs better than the uninitialized simulations mostly due to contributions during the positive AMO phase driven by the subset skill score. Compared to the low-resolution system (preop-LR), no overall performance benefits are made in this region, but positive contributions are achieved for initialization in neutral AMO phases. Additionally, the decomposition reveals a strong imbalance among the subsets (defined by AMO phases) in terms of reference weighting, allowing for insightful interpretation and conclusions. This skill score decomposition framework for conditional verification is a valuable tool to analyze the effect of physical processes on forecast performance and, consequently, supports model development and the improvement of operational forecasts.

Breathing chimera states in nonlocally coupled type-I excitable phase oscillators

Breathing chimera states in nonlocally coupled type-I excitable phase oscillators

Inferring noise intensity and phase response from noisy synchronous oscillators

Numerous biological and microscale systems exhibit synchronization in noisy environments. The theory of such noisy oscillators and their synchronization has been developed and experimentally demonstrated, but inferring the noise intensity and phase response is not always straightforward. In this paper, we propose a useful formula that enables us to infer the noise intensity and phase response of a noisy oscillator synchronized with periodic external forcing. Through asymptotic approximations for small noise, we show that noisy synchronous oscillators satisfy a simple relationship among the noise intensity and measurable quantities, i.e., the stationary distribution of the oscillation phase and stationary probability current obtained as the average phase velocity, which is verified through systematic numerical analysis. The proposed formula facilitates a unified analysis and design of synchronous oscillators in weakly noisy environments. Published by the American Physical Society 2025

Causal evidence for increased theta and gamma phase consistency in a parieto-frontal network during the maintenance of visual attention.

Endogenous visuo-spatial attention is under the control of a fronto-parietal network of brain regions. One key node in this network, the intra-parietal sulcus (IPS), plays a crucial role in maintaining endogenous attention, but little is known about its ongoing physiology and network dynamics during different attentional states. Here, we investigated the reactivity of the left IPS in response to brain stimulation under different states of selective attention. We recorded electroencephalography (EEG) in response to single pulses of transcranial magnetic stimulation (TMS) of the IPS, while participants (N=44) viewed bilateral random-dot motion displays. Individual MRI-guided TMS pulses targeted the left IPS, while the left primary somatosensory cortex (S1) served as an active control site. In separate blocks of trials, participants were cued to attend covertly to the motion display in one hemifield (left or right) and to report brief coherent motion targets. The perceptual load of the task was manipulated by varying the degree of motion coherence of the targets. Excitability, variability and information content of the neural responses to TMS were assessed by analysing TMS-evoked potential (TEP) amplitude and inter-trial phase clustering (ITPC), and by performing multivariate decoding of attentional state. Results revealed that a left posterior region displayed reduced variability in the phase of theta and gamma oscillations following TMS of the IPS, but not of S1, when attention was directed contralaterally, rather than ipsilaterally to the stimulation site. A right frontal cluster also displayed reduced theta variability and increased amplitude of TEPs when attention was directed contralaterally rather than ipsilaterally, after TMS of the IPS but not S1. Reliable decoding of attentional state was achieved after TMS pulses of both S1 and IPS. Taken together, our findings suggest that endogenous control of visuo-spatial attention leads to changes in the intrinsic oscillatory properties of the IPS and its associated fronto-parietal network.

Resonant enhancement and confinement of microwave field in coupled conductive rod systems

Abstract We investigated the resonant interaction of incident microwaves with a finite linear array of equidistantly arranged conductive rods of finite height. When strong coupling is established between adjacent rods, which act as open resonators for radial waves, a series of resonances emerges, corresponding to the number of rods in the array. Each resonance exhibits distinct charge oscillation amplitudes and phases along the rods, leading to varying radiative losses. Notably, in a system of two resonantly interacting rods, antiphase charge oscillations result in a nearly 30-fold increase in localized field intensity and a quality factor of approximately 400. This study demonstrates the feasibility of creating high-quality open resonators with sub-wavelength confinement, offering the potential for microwave-to-optical conversion and enabling control over quantum processes in materials, thereby broadening their application scope.

Individualized temporal patterns drive human sleep spindle timing

Sleep spindles are cortical electrical oscillations considered critical for memory consolidation and sleep stability. The timing and pattern of sleep spindles are likely to be important in driving synaptic plasticity during sleep as well as preventing disruption of sleep by sensory and internal stimuli. However, the relative importance of factors such as sleep depth, cortical up/down-state, and temporal clustering in governing sleep spindle dynamics remains poorly understood. Here, we analyze sleep data from 1,025 participants, statistically modeling the simultaneous influences of multiple factors on moment-to-moment spindle production using a point process-generalized linear model framework. Results reveal fingerprint-like timing patterns, characterized by a refractory period followed by a period of increased spindle activity, which are highly individualized yet consistent night-to-night, with increased variability with age. Strikingly, short-term (<15 s) temporal patterns of past spindle history are the main determinant of spindle timing, accounting for over 70% of the statistical deviance-surpassing the contribution of factors such as cortical up/down-state (slow oscillation phase), sleep depth, and long-term history (15 to 90 s, including ~50 s infraslow activity). Short-term history has a statistically significant influence in over 98% of the population, suggesting it is a near-universal feature of spindle activity. Short-term history and slow oscillation phase exert independent effects on spindle timing. Our results establish a robust statistical framework to examine abnormalities in sleep spindle timing observed in neurological disorders and aging, as well as the relationship between individualized sleep spindle timing, cognition, and sleep stability.

Detection of respiratory frequency rhythm in human alpha phase shifts: topographic distributions in wake and drowsy states.

The relationship between brain activity and respiration is recently attracting increasing attention, despite being studied for a long time. Respiratory modulation was evidenced in both single-cell activity and field potentials. Among EEG and intracranial measurements, the effect of respiration was prevailingly studied on amplitude/power in all frequency bands. Since phases of EEG oscillations received less attention, we applied our previously published carrier frequency (CF) mathematical model of human alpha oscillations on a group of 10 young healthy participants in wake and drowsy states, using a 14-channel average reference montage. Since our approach allows for a more precise calculation of CF phase shifts (CFPS) than any individual Fourier component, by using a 2-s moving Fourier window, we validated the new method and studied, for the first time, temporal waveforms CFPS(t) and their oscillatory content through FFT (CFPS(t)). Although not appearing equally in all channel pairs and every subject, a clear peak in the respiratory frequency region, 0.21-0.26Hz, was observed (max at 0.22Hz). When five channel pairs with the most prominent group averaged amplitudes at 0.22Hz were plotted in both states, topographic distributions changed significantly-from longitudinal, connecting frontal and posterior channels in the wake state to topographically split two separate regions-frontal and posterior in the drowsy state. In addition, in the drowsy state, 0.22-Hz amplitudes decreased for all pairs, while statistically significant reduction was obtained for 20/91 (22%) pairs. These results potentially evidence, for the first time, the respiratory frequency modulation of alpha phase shifts, as well as the significant impact of wakeful consciousness on the observed oscillations.

Strength of Low-Frequency EEG Phase Entrainment to External Stimuli Is Associated with Fluctuations in the Brain's Internal State.

The brain attends to environmental rhythms by aligning the phase of internal oscillations. However, the factors underlying fluctuations in the strength of this phase entrainment remain largely unknown. In the present study, we examined whether the strength of low-frequency electroencephalography (EEG) phase entrainment to rhythmic stimulus sequences varied with the pupil size and posterior alpha-band power, thought to reflect the arousal level and excitability of posterior cortical brain areas, respectively. We recorded the pupil size and scalp EEG while participants carried out an intermodal selective attention task, in which they were instructed to attend to a rhythmic sequence of visual or auditory stimuli and ignore the other perceptual modality. As expected, intertrial phase coherence (ITC), a measure of entrainment strength, was larger for the task-relevant than for the task-irrelevant modality. Across the experiment, the pupil size and posterior alpha power were strongly linked with each other. Interestingly, ITC tracked both variables: larger pupil size was associated with a selective increase in entrainment to the task-relevant stimulus sequence, whereas larger posterior alpha power was associated with a decrease in phase entrainment to both the task-relevant and task-irrelevant stimulus sequences. Exploratory analyses showed that a temporal relation between ITC and posterior alpha power emerged in the time periods around pupil maxima and pupil minima. These results indicate that endogenous sources contribute distinctly to the fluctuations of EEG phase entrainment.

Mean-field approximation for networks with synchrony-driven adaptive coupling.

Synaptic plasticity plays a fundamental role in neuronal dynamics, governing how connections between neurons evolve in response to experience. In this study, we extend a network model of θ-neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of θ-neuron oscillators. We explore two distinct implementations of this plasticity: pairwise updates to individual coupling strengths and global updates applied to the mean coupling strength. We derive a mean-field approximation and assess its accuracy by comparing it to θ-neuron simulations across various stability regimes. The synchrony of the system is quantified using the Kuramoto order parameter. Through bifurcation analysis and the calculation of maximal Lyapunov exponents, we uncover interesting phenomena such as bistability and chaotic dynamics via period-doubling and boundary crisis bifurcations. These behaviors emerge as a direct result of adaptive coupling and are absent in systems without such plasticity.

A Comparative Investigation of Monsoon Active and Break Events over the Western North Pacific

Abstract This study identifies 86 active events and 66 break events of the western North Pacific summer monsoon (WNPSM) from 1979 to 2020. These active and break events exhibit sharp contrast in large-scale convection and circulation fields. During the active period, deep convection almost covers the entire WNP domain (0°–25°N, 120°–170°E), accompanied by the strengthening of a local monsoon trough and monsoon westerlies extending from the Arabian Sea to the WNP. In contrast, during the break period, along with weakened monsoon westerlies, the subtropical high replaces the monsoon trough to dominate the WNP domain, leading to the disappearance of deep convection. Results about the convection evolution at multiple time scales indicate that active/break events are primarily contributed to by the wet/dry phases of intraseasonal oscillations (ISOs). The phase transitions of ISOs are nearly symmetric between active and break events. However, these two types of events present notable asymmetric features in convection anomalies relative to climatology, which can be attributable to the modulation of the seasonal mean component. Specifically, both active and break events correspond to anomalously strong seasonal mean convection, which amplifies (weakens) the convection enhancement (suppression) during the active (break) period and results in normal (enhanced) convection during adjacent periods. The preferred occurrence of active and break events in strong summer monsoons is because related mean backgrounds, including increased low-level positive vorticity, specific humidity, and easterly vertical shear, facilitate the intensification of ISOs. These mean backgrounds are likely induced by SST cooling in the north Indian Ocean and warming in the equatorial central Pacific during the simultaneous summer. Significance Statement The subseasonal variation in monsoon rainfall typically manifests as fluctuations between active events with abundant rainfall and break events with deficit rainfall, which can induce converse extremes such as floods and droughts, significantly affecting water management, agriculture planning, and economic activities. This study aims to reveal the characteristics, formation, and occurrence regularity of active and break events during the western North Pacific summer monsoon (WNPSM). We note that the occurrence of these active and break events is determined not only by intraseasonal oscillations but also by seasonal mean backgrounds, which result in certain asymmetrical features between the two types of events. These results will enhance our understanding of the monsoon’s intraseasonal variability and the physical association between multiple time scales over the WNP domain (0°–25°N, 120°–170°E).

A Machine Learning Approach for Filling Long Gaps in Eddy Covariance Time Series Data in a Tropical Dry Forest

AbstractLong‐term eddy covariance (EC) data are crucial for understanding the impact of global change on ecosystem functions. However, EC data often contain long gaps, particularly in tropical dry forests (TDF) due to seasonality and El Niño‐Southern Oscillation (ENSO) phases. These factors create high variability, complex dependencies, and dynamic flux footprints. No current gap‐filling method adequately addresses long gaps in TDFs. This study introduces a novel framework for addressing this issue by (a) defining gap sizes by their relative percentages, (b) training, tuning, and evaluating two machine learning (ML) models: MissForest for short gaps and Prophet for intermediate and long gaps, and (c) predicting half‐hourly EC data from 2013 to 2022 for six EC variables, where actual gap data sets ranged from 26.6% to 28.4%, at TDF in Costa Rica. Results indicate that MissForest excelled at filling short gaps (≤5%, R2 = 0.76 and Nash‐Sutcliffe efficiency (NSE) = 0.71), while Prophet performed exceptionally well for gaps between 5% and 10% (R2 = 0.72 and NSE = 0.67). However, both models struggled with gaps between 10% and 13%. Validation showed R2 values of 0.79, 0.88, and 0.77 for CO₂ flux, sensible heat flux, and latent heat flux, respectively, with corresponding NSE values of 0.78, 0.86, and 0.72, and normalized root mean squared error (NRMSE) around 2E‐4. Additionally, to validate our results, we applied our approach at three EC sites with different ecological conditions, demonstrating robust performance. This study presents a reliable ML approach for imputing long gaps in EC data, which can be applied to sites with strong variability.

TMS-induced modulation of brain networks and its associations to rTMS treatment for depression: a concurrent fMRI-EEG-TMS study.

Transcranial magnetic stimulation (TMS) over the left dorsolateral prefrontal cortex (L-DLPFC) is an established intervention for treatment-resistant depression (TRD), yet the underlying therapeutic mechanisms remain not fully understood. This study employs an integrative approach that combines TMS with concurrent functional magnetic resonance imaging (fMRI) and electroencephalography (EEG), aimed at assessing the acute/immediate effects of TMS on brain network dynamics and their correlation with clinical outcomes. Our study demonstrates that TMS acutely modulates connectivity within vital brain circuits, particularly the cognitive control and default mode networks. We found that the baseline TMS-evoked responses in the cognitive control and limbic networks significantly predicted clinical improvement in patients receiving a novel EEG-synchronized repetitive TMS treatment. Furthermore, this study explored the brain-state dependent effects of TMS, as the brain-state indexed by the phase of EEG prefrontal alpha oscillation. We found that clinical outcomes in this novel treatment are linked to state-specific TMS-modulated functional connectivity within a pivotal brain circuit of the L-DLPFC and the posterior subgenual anterior cingulate cortex within the limbic system. These findings contribute to our understanding of the therapeutic effects underlying TMS treatment in depression and support the potential of assessing state-dependent TMS effects in TMS timing target selection. This study emphasizes the importance of personalized timing of TMS for optimizing target engagement of specific clinically relevant brain circuits. Our results are crucial for future research into the development of personalized neuromodulation therapies for TRD patients.

Analysis of equilibria in a ring of phase oscillators with nearest-neighbor and next-nearest-neighbor interactions

Analysis of equilibria in a ring of phase oscillators with nearest-neighbor and next-nearest-neighbor interactions