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This study numerically investigates the influence of the taper on the flow-induced vibrations of an elastically mounted circular cylinder under vortex-induced vibrations (VIV). The dynamic response of three different taper ratios [ T R defined as T R = l / (d 2 − d 1) = 12 (highly tapered cylinder), 20 (medium tapered cylinder), and 40 (low tapered cylinder)], where d1 and d2 are the largest and smallest diameter of the tapered cylinder, respectively, with length l is studied at a fixed Reynolds number [ Re D , defined based on the averaged cylinder diameter, D = (d 1 + d 2) / 2 ] of 150. The amplitude and frequency response of the tapered cylinder is characterized by a low mass ratio (defined as the ratio of the total oscillating mass to the displaced fluid mass) of m* = 2 over the wide range of reduced velocity (3 ≤ U r ≤ 16) covering the full amplitude-response spectrum (based on the oscillation amplitude) of the VIV. The results show the existence of difference in the spanwise shedding of vortices owing to the poor spanwise pressure correlation. The flow field analysis in the wake of the oscillating cylinder reveals the dominance of the three-dimensional structures in the wake (near the top end with the larger diameter) behind the cylinder with the increase in the taper ratio (even at such low Re D where the uniform cylinder exhibits the two-dimensional wake). Also, the tapered cylinder exhibits a wide range of frequency synchronization (i.e., wide lock-in area) compared to the uniform cylinder. Tapering the cylinder results in the shift of the peak of the max oscillation amplitude or, in turn, the shift in the transitioning of the response branches. Further, force decomposition, energy transfer, and phase dynamics are also discussed for the taper cylinders. [ABSTRACT FROM AUTHOR]

We study fast and slow clustering dynamics of Cucker–Smale ensemble with internal phase dynamics via the Cucker–Smale–Kuramoto (in short, CSK) model. The CSK model describes the emergent dynamics of flocking particles with phase dynamics. It consists of the Cucker–Smale flocking model and the Kuramoto model, and their interplay is registered in the communication weight function between particles. We present a sufficient framework for mono-cluster flocking and complete synchronization in terms of system parameters and initial data. In particular, the mono-cluster flocking will emerge exponentially fast (fast dynamics). On the other hand, when initial spatial-velocity configuration is close to the bi-cluster flocking, we also provide a sufficient framework leading to convergence of bi-cluster flocking algebraically slow depending on the decay rate of the communication weight (slow flocking dynamics). We also provide several numerical examples and compare them with analytical results. [ABSTRACT FROM AUTHOR]

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise. [ABSTRACT FROM AUTHOR]

Neural interactions occur on different levels and scales. It is of particular importance to understand how they are distributed among different neuroanatomical and physiological relevant brain regions. We investigated neural cross-frequency couplings between different brain regions according to the Desikan–Killiany brain parcellation. The adaptive dynamic Bayesian inference method was applied to EEG measurements of healthy resting subjects in order to reconstruct the coupling functions. It was found that even after averaging over all subjects, the mean coupling function showed a characteristic waveform, confirming the direct influence of the delta-phase on the alpha-phase dynamics in certain brain regions and that the shape of the coupling function changes for different regions. While the averaged coupling function within a region was of similar form, the region-averaged coupling function was averaged out, which implies that there is a common dependence within separate regions across the subjects. It was also found that for certain regions the influence of delta on alpha oscillations is more pronounced and that oscillations that influence other are more evenly distributed across brain regions than the influenced oscillations. When presenting the information on brain lobes, it was shown that the influence of delta emanating from the brain as a whole is greatest on the alpha oscillations of the cingulate frontal lobe, and at the same time the influence of delta from the cingulate parietal brain lobe is greatest on the alpha oscillations of the whole brain. [ABSTRACT FROM AUTHOR]

Synaptically coupled neurons show in-phase or antiphase synchrony depending on the chemical and dynamical nature of the synapse. Deterministic theory helps predict the phase differences between two phase-locked oscillators when the coupling is weak. In the presence of noise, however, deterministic theory faces difficulty when the coexistence of multiple stable oscillatory solutions occurs. We analyze the solution structure of two coupled neuronal oscillators for parameter values between a subcritical Hopf bifurcation point and a saddle node point of the periodic branch that bifurcates from the Hopf point, where a rich variety of coexisting solutions including asymmetric localized oscillations occurs. We construct these solutions via a multiscale analysis and explore the general bifurcation scenario using the λ-ω model. We show for both excitatory and inhibitory synapses that noise causes important changes in the phase and amplitude dynamics of such coupled neuronal oscillators when multiple oscillatory solutions coexist. Mixed-mode oscillations occur when distinct bistable solutions are randomly visited. The phase difference between the coupled oscillators in the localized solution, coexisting with in-phase or antiphase solutions, is clearly represented in the stochastic phase dynamics. [ABSTRACT FROM AUTHOR]

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, f1 and f2. On increasing the forcing amplitude, xf, at a fixed forcing frequency, ff, we find two different types of synchronization: (i) ff/f1 = 1: 1 or 2: 1 chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to 1: 1 CDS, the system transitions from an unforced chaotic state (CH1,2) to a forced chaotic state (CH1,2,f), then to a two-frequency quasiperiodic state where chaos is destroyed (T²2,f), and finally to a phase-locked period-1 state (P1f). The route to 2: 1 CDS is similar, but the quasiperiodic state hosts a doubled torus (2T²2,f) that transforms into a phase-locked period-2 orbit (P2f) when CDS occurs. En route to PSC, the system transitions to a forced chaotic state (CH1,2,f) followed by a phase-locked chaotic state, where f1, f2 and ff still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical xf required for the onset of CDS does not vary significantly with ff. We then use two unidirectionally coupled Anishchenko-Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to 1: 1 CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the ff/f1-xf plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control. [ABSTRACT FROM AUTHOR]

We have simulated a chain of sinoatrial pacemaker cells connected via gap junctions. To study the dynamics we introduce a phase of oscillations and show that Burgers equation is adequate to describe the phase dynamics in the sinoatrial node. We show that the propagating action potential bears properties of either trigger waves, or phase waves, which depends upon its wave number. We propose a definition of the safety factor that is applicable to the oscillatory tissue of the sinoatrial node and show that the maximum of the safety factor relates to the boundary case separating phase waves and trigger waves. [ABSTRACT FROM AUTHOR]

A two-dimensional D-shaped cylinder and heaving foil were mounted in tandem and used to simulate the main body and tail, respectively, of a natural swimmer. Thrust/drag measurements of the force on the foil and particle image velocimetry measurements of the flow downstream of the swimming system were conducted at a Reynolds number of about $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}10^4$ in a water channel with a constant free stream current speed. Two main sets of measurements were conducted: one set with the swimming system locked at a fixed streamwise location in the water channel as the heave frequency of the foil was varied; the other set with the system freely swimming to a desired set-point position from different upstream and downstream locations. When the freely swimming system reached and maintained its set-point position, so that its swimming speed matched that of the current, the oscillation frequency of the heaving foil corresponded to a Strouhal number of 0.36. Phase portraits of the measured thrust/drag forces reveal limit cycle oscillations for all swimming cases studied, which suggests that self-regulation drives the selection of this Strouhal number. No coupling was observed between the vortices shed by the D-shaped cylinder and the self-selected frequency of the heaving foil during free swimming. An examination of the ratio of the phase-locking indices for the input heaving motion of the foil and the coupled fluidic thrust/drag response reveals that it approaches a value of 0.5 over time when the freely swimming system is released from rest and allowed to achieve steady-state cruising. The jet produced by the freely swimming foil was inclined at an angle of approximately $4^\circ $ with respect to the direction of the mean flow. [ABSTRACT FROM PUBLISHER]

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which m: n frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation. [ABSTRACT FROM AUTHOR]

In this paper we extend the results of Frankel and Kiemel [SIAM J. Appl. Math, 53 (1993), pp. 1436-1446] to a network of slowly coupled oscillators. First, we use Malkin's theorem to derive a canonical phase model that describes synchronization properties of a slowly coupled network. Then, we illustrate the result using slowly coupled oscillators (1) near Andronov-Hopf bifurcations, (2) near saddle-node on invariant circle bifurcations, and (3) near relaxation oscillations. We compare and contrast synchronization properties of slowly and weakly coupled oscillators. [ABSTRACT FROM AUTHOR]

The brain is a complex non-equilibrium system capable of expressing many different dynamics as well as the transitions between them. We hypothesized that the level of non-equilibrium can serve as a signature of a given brain state, which was quantified using the arrow of time (the level of irreversibility). Using this thermodynamic framework, the irreversibility of emergent cortical activity was quantified from local field potential recordings in male Lister-hooded rats at different anesthesia levels and during the sleep-wake cycle. This measure was carried out on five distinct brain states: slow-wave sleep, awake, deep anesthesia–slow waves, light anesthesia–slow waves, and microarousals. Low levels of irreversibility were associated with synchronous activity found both in deep anesthesia and slow-wave sleep states, suggesting that slow waves were the state closest to the thermodynamic equilibrium (maximum symmetry), thus requiring minimum energy. Higher levels of irreversibility were found when brain dynamics became more asynchronous, for example, in wakefulness. These changes were also reflected in the hierarchy of cortical dynamics across different cortical areas. The neural dynamics associated with different brain states were characterized by different degrees of irreversibility and hierarchy, also acting as markers of brain state transitions. This could open new routes to monitoring, controlling, and even changing brain states in health and disease. [ABSTRACT FROM AUTHOR]

The brain is a complex non-equilibrium system capable of expressing many different dynamics as well as the transitions between them. We hypothesized that the level of non-equilibrium can serve as a signature of a given brain state, which was quantified using the arrow of time (the level of irreversibility). Using this thermodynamic framework, the irreversibility of emergent cortical activity was quantified from local field potential recordings in male Lister-hooded rats at different anesthesia levels and during the sleep-wake cycle. This measure was carried out on five distinct brain states: slow-wave sleep, awake, deep anesthesia–slow waves, light anesthesia–slow waves, and microarousals. Low levels of irreversibility were associated with synchronous activity found both in deep anesthesia and slow-wave sleep states, suggesting that slow waves were the state closest to the thermodynamic equilibrium (maximum symmetry), thus requiring minimum energy. Higher levels of irreversibility were found when brain dynamics became more asynchronous, for example, in wakefulness. These changes were also reflected in the hierarchy of cortical dynamics across different cortical areas. The neural dynamics associated with different brain states were characterized by different degrees of irreversibility and hierarchy, also acting as markers of brain state transitions. This could open new routes to monitoring, controlling, and even changing brain states in health and disease. [ABSTRACT FROM AUTHOR]

When exposed to rhythmic stimulation, the human brain displays rhythmic activity across sensory modalities and regions. Given the ubiquity of this phenomenon, how sensory rhythms are transformed into neural rhythms remains surprisingly inconclusive. An influential model posits that endogenous oscillations entrain to external rhythms, thereby encoding environmental dynamics and shaping perception. However, research on neural entrainment faces multiple challenges, from ambiguous definitions to methodological difficulties when endogenous oscillations need to be identified and disentangled from other stimulus-related mechanisms that can lead to similar phase-locked responses. Yet, recent years have seen novel approaches to overcome these challenges, including computational modeling, insights from dynamical systems theory, sophisticated stimulus designs, and study of neuropsychological impairments. This review outlines key challenges in neural entrainment research, delineates state-of-the-art approaches, and integrates findings from human and animal neurophysiology to provide a broad perspective on the usefulness, validity, and constraints of oscillatory models in brain–environment interaction. [ABSTRACT FROM AUTHOR]

Abstract. Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, antiphase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions... [ABSTRACT FROM AUTHOR]

Biological processes are governed by the expression of proteins, and for some proteins, their level of expression can fluctuate periodically over time (i.e., they oscillate). Many oscillatory proteins (e.g., cell cycle proteins and those from the HES family of transcription factors) are connected in complex ways, often within large networks. This complexity can be elucidated by developing intuitive mathematical models that describe the underlying critical aspects of the relationships between these processes. Here, we provide a mathematical explanation of a recently discovered biological phenomenon: the phasic position of the gene Hes1's oscillatory expression at the beginning of the cell cycle of an individual human breast cancer stem cell can have a predictive value on how long that cell will take to complete a cell cycle. We use a two-component model of coupled oscillators to represent Hes1 and the cell cycle in the same cell with minimal assumptions. Inputting only the initial phase angles, we show that this model is capable of predicting the dynamic mitosis to mitosis behaviour of Hes1 and predicting cell cycle length patterns as found in real-world experimental data. Moreover, we discover that bidirectional coupling between Hes1 and the cell cycle is critical within the system for the data to be reproduced and that nonfixed asymmetry in the interactions between the oscillators is required. The phase dynamics we present here capture the complex interplay between Hes1 and the cell cycle, helping to explain nongenetic cell cycle variability, which has critical implications in cancer treatment contexts. [ABSTRACT FROM AUTHOR]

Polymer gels undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction are one of the few synthetic materials that exhibit biomimetic mechano-chemical transduction, converting mechanical input into chemical energy. Here, we consider self-oscillating BZ gels that are subjected to periodic mechanical forcing, and model the entrainment of the oscillatory gel dynamics to this external stimulus. The gel size is assumed to be sufficiently small that the chemo-mechanical oscillations are spatially uniform. The behavior of the system is captured by equations describing the kinetics of the oscillatory BZ reaction in the gel coupled to equations for the variations in gel size due to the inherent reaction and imposed force. We employ the phase dynamics approach for analyzing the entrainment of the BZ gel to force- and strain-controlled compressive deformations. The phase response curves are obtained using Malkin's method, and time-averaging is applied to extract the slow phase dynamics caused by the periodic forcing. We demonstrate that the entrainment of the self-oscillating BZ gel is sensitive to the chemo-mechanical coupling in gel, the mode of deformation, and the level of static compression. Kuramoto's model of phase oscillators is shown to be applicable if the external forcing is purely harmonic. [ABSTRACT FROM AUTHOR]

A forward modeling technique is developed for determining the characteristic features of observed MHD modes from the line-of-sight data of the soft x-ray (SXR) tomography diagnostics in the Wendelstein 7-X (W7-X) stellarator. In particular, forward modeling is used to evaluate the poloidal mode numbers m, radial location, poloidal rotation direction and ballooning character of the MHD modes. The poloidal mode structures have been modeled by the radially localized Gaussian-shaped emission regions rotating along the magnetic surfaces. In the present study the cases of rigid-shape emission regions and flexible emission regions are modeled. Various mode phase velocity dependences on the magnetic surface position are simulated. The modeled phase dynamics of line-integrated oscillations and the distribution of oscillation amplitudes are compared with the experimental signals of the SXR cameras which observe the plasma at various viewing angles in the poloidal cross-section. Application of this technique enables describing of the 1–50 kHz modes. In particular, in the discharge W7X-PID 20180918.045 three identified branches with the poloidal mode numbers m= 8, m= 10 and m= 11 localized at ρ ≈ 0.3 are rotating in the clockwise poloidal direction. The present paper reports the first application of the forward modeling technique to the data from the SXR diagnostics in W7-X. The high m-modes are identified by forward modeling in W7-X. [ABSTRACT FROM AUTHOR]

Synchronous oscillations are ubiquitous throughout the cortex, but the frequency of oscillations differs from area to area. To elucidate the mechanistic architectures underlying various rhythmic activities, we tested whether spontaneous neural oscillations in different local cortical areas and large-scale networks can be phase-entrained by direct perturbation with distinct frequencies of repetitive transcranial magnetic stimulation (rTMS). While recording the electroencephalogram (EEG), we applied single-pulse TMS (sp-TMS) and rTMS at 5, 11, and 23 Hz over the motor or visual cortex. We assessed local and global modulation of phase dynamics using the phase-locking factor (PLF). sp-TMS to the motor and the visual cortex triggered a transient increase in PLF in distinct frequencies that peaked at 21 and 8 Hz, respectively. rTMS at 23 Hz over the motor cortex and 11 Hz over the visual cortex induced a prominent and progressive increase in PLF that lasted for a few cycles after the termination of rTMS. Moreover, the local increase in PLF propagated to other cortical areas. These results suggest that distinct cortical areas have area-specific oscillatory frequencies, and the manipulation of oscillations in local areas impacts other areas through the large-scale oscillatory network with the corresponding frequency specificity. We speculate that rTMS that is close to area-specific frequencies (natural frequencies) enables direct manipulation of brain dynamics and is thus useful for investigating the causal roles of synchronous neural oscillations. Moreover, this technique could be used to treat clinical symptoms associated with impaired oscillations and synchrony. [ABSTRACT FROM AUTHOR]

We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized. [ABSTRACT FROM AUTHOR]

Neuronal oscillations are commonly analyzed with power spectral methods that quantify signal amplitude, but not rhythmicity or 'oscillatoriness' per se. Here we introduce a new approach, the phase-autocorrelation function (pACF), for the direct quantification of rhythmicity. We applied pACF to human intracerebral stereoelectroencephalography (SEEG) and magnetoencephalography (MEG) data and uncovered a spectrally and anatomically fine-grained cortical architecture in the rhythmicity of single- and multi-frequency neuronal oscillations. Evidencing the functional significance of rhythmicity, we found it to be a prerequisite for long-range synchronization in resting-state networks and to be dynamically modulated during event-related processing. We also extended the pACF approach to measure 'burstiness' of oscillatory processes and characterized regions with stable and bursty oscillations. These findings show that rhythmicity is double-dissociable from amplitude and constitutes a functionally relevant and dynamic characteristic of neuronal oscillations. Myrov and colleagues introduce a novel method to measure the rhythmicity of neuronal oscillations and demonstrating that the oscillatory architecture of the human cortex is spectrally sparse and anatomically well delineated. [ABSTRACT FROM AUTHOR]

Previous research has delved into the brain's response to top-down and bottom-up conflicts in numerical inductive reasoning. However, the specific neural oscillatory patterns associated with these conflict types in numerical inductive reasoning processing have remained elusive. In this study, we employed a number series completion task in which participants had to determine whether a given target number adhered to concealed rules. Three conditions were established: an identity condition (e.g., 13, 13, 13), a perceptual mismatch condition (representing bottom-up conflict, e.g., 13 13 + 三), and a rule violation condition (representing top-down conflict, e.g., 13 13 14). Our EEG results revealed significant distinctions: rule violation induced more pronounced alpha desynchronization compared to both perceptual mismatch and identity conditions. Conversely, perceptual mismatch was associated with increased theta synchronization in contrast to rule violation and the identity condition. These findings suggest that alpha desynchronization may indicate the integration of rules during top-down conflict, while theta synchronization may function as a mechanism to inhibit bottom-up perceptual interference in numerical inductive reasoning. [ABSTRACT FROM AUTHOR]

This paper presents a peculiar nodal-shaped oscillation in vortex-induced vibration (VIV). This response is distinct from the commonly observed limit cycle oscillation in VIV and other aeroelastic problems. To gain insight into the dynamics in nodal-shaped oscillation, we conduct wind tunnel tests to investigate the VIV response of a freely oscillating rectangular cylinder with various transverse structural natural frequencies fs and wind speeds. The evolution of the flow field during nodal-shaped oscillation was examined using time-frequency analysis and modal analysis. During the divergent stage of the nodal-shaped oscillation, two modes, namely, the wake mode with a frequency of f = 1.28fs and the structure mode with a frequency of f = fs, were found to dominate the response of the flow. The two modes in VIV are coupled and compete with each other, diverging the oscillation of the structure. As the oscillation diverges and the amplitude increases to the maximum, the wake mode vanishes, which disengages the coupling of the fluid and structure modes. This stops the VIV and the oscillation decays until the wake mode reappears at f = 1.28fs. The above processes cycle over and over again, resulting in nodal-shaped (divergent-decay-divergent-decay) oscillation cycles. This finding explains the underlying dynamical mechanism of nodal-shaped oscillation and demonstrates the strong relationship between the wake mode and VIV. [ABSTRACT FROM AUTHOR]

We consider a system of coupled swarmalators moving in two dimensional space and explore its collective behavior. Here the swarmalators represent the oscillators that can sync and swarm in space, following the previous study [O'Keeffe et al., Nat. Commun., 8, 1504 (2017)]. The internal state of each swarmalator is represented by its phase angle, and the swarmalators are free to move in the plane according to an equation of motion where the phase and spatial dynamics are coupled with each other. In particular, the phase coupling between the swarmalators is attractive (positive) one, so the coupling makes the swarmalators have their phase difference minimized. The collective behavior of the system is found to be different depending on the extent of the interplay between the phase and spatial dynamics: Specifically, when the extent of the interplay between the phase and spatial dynamics is so weak as to be negligible, the phase dynamics of our system recovers that of the conventional mean-field X Y model. On the other hand, when a certain extent of the interplay is present, the system is found to exhibit the correlated phase where the overall order does not occur. Interestingly, it is found that the correlated phase is the same as the active phase wave found in the system of swarmalators with repulsive phase coupling [O'Keeffe et al., Nat. Commun., 8, 1504 (2017)]. We also find that the system exhibits two different phase transitions: One is the transition from the sync state to the active phase wave state, and the other one is the transition from the active phase wave state to the async state. We perform the finite-size scaling analysis and investigate the transition nature. [ABSTRACT FROM AUTHOR]

We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the limit cycle but also deviations from it by introducing amplitude variables and using them with the phase variable. The framework allows us to study how networks react to applied inputs or coupling, including their synchronization and phase locking, while capturing the deviations of the network states from the unperturbed dynamics. Numerical simulations are used to demonstrate the effectiveness of the framework for networks composed of FitzHugh–Nagumo elements. The resulting phase-amplitude equations can be used in deriving optimal periodic waveforms or introducing feedback control for achieving fast phase locking while stabilizing the collective oscillations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel communication timing control for wireless sensor networks, named Phase Diffusion Time Division method. This is based on the mutual synchronization of coupled phase oscillatory dynamics with a stochastic adaptation, according to the history of collision frequency in communication nodes. Through local and fully distributed interactions in the communication network, the coupled phase dynamics self-organizes an efficient time division pattern of the communication so that the network reduces the collision frequency by diffusion of the phase pattern, while it sustains sufficient throughput of the communications. We introduce the built-in virtual node dynamics model for sensor device, to implement impulse signal based interactions. This method is designed for applications in a regular grid model of the wireless network, but it can be extended to an irregular grid model as simulation results illustrate, where the proposed method outperforms CSMA method in the efficiency. [ABSTRACT FROM AUTHOR]

Paranormal believers' thinking is frequently biased by intuitive beliefs. Lack of inhibition of these tempting beliefs is considered a key element in paranormal believers' thinking. However, the brain activity related to inhibitory control in paranormal believers is poorly understood. We examined EEG activities at resting state in alpha, beta, and gamma bands with inhibitory control in paranormal believers and skeptics. The present study shows that paranormal belief is related to the reduced power of the alpha, beta, and gamma frequency bands, and reduced inhibitory control. This study may contribute to understanding the differences between believers and skeptics in brain activity related to inhibitory control in paranormal believers. [ABSTRACT FROM AUTHOR]

A change in the human psychophysiological state, caused by stress in particular, affects the processes of autonomic control, the activity of which is reflected in infra-slow oscillations of brain potentials with a frequency of less than 0.5 Hz. We studied the infra-slow oscillations in scalp electroencephalogram (EEG) signals in the frequency ranges of 0.05–0.15 Hz and 0.15–0.50 Hz that are associated with the processes of sympathetic and parasympathetic control, respectively, in healthy subjects at rest and during stress-inducing cognitive tasks. The power spectra of EEG signals, the phase coherence coefficients, and indices of directional coupling between the infra-slow oscillations in the signals of different EEG leads were analyzed. We revealed that, compared with the state of rest, the stress state is characterized by a significant decrease in the power of infra-slow oscillations and changes in the structure of couplings between infra-slow oscillations in EEG leads. In particular, under stressful conditions, a decrease in both intrahemispheric and interhemispheric coupling between EEG leads occurred in the range of 0.05–0.15 Hz, while a decrease in intrahemispheric and an increase in interhemispheric couplings was observed in the range of 0.15–0.50 Hz. [ABSTRACT FROM AUTHOR]

Interactions between a couple of flames often lead to their synchronisation. Flame–flame interaction has recently been linked with thermoacoustic instability in combustors. However, synchronisation caused by the interaction of coupled flames is still not fully understood. Furthermore, the interacting flame oscillators in practical situations often have a slight dissimilarity between them. Here, we systematically study the effects of such dissimilarity on the flame–flame interaction with a simple system consisting of two candle flame oscillators (CFO). The interaction is studied with CFOs having similar and dissimilar amplitudes of oscillations. The distance between the CFOs is parametrically varied. The results indicate that the synchronisation phenomena caused by flame–flame interaction have a complex dependence on the distance between the oscillators. Further, we find the flame–flame interaction to be significantly affected by the dissimilarity of the interacting oscillators. In-phase (IP) synchronisation occurs when the interacting oscillators are separated by a low distance and the oscillators have similar or moderately dissimilar amplitudes of oscillations. On the other hand, for large disparities in the amplitudes of oscillations, lag synchronisation (LS) is observed at a low distance between the CFOs. If the interacting oscillators have similar amplitudes of oscillations, the amplitude death (AD) regime persists throughout the operating range except at a low distance between the CFOs. In contrast, if the interacting oscillators have dissimilar amplitudes of oscillations, different rich dynamical states such as lag synchronisation and partial amplitude death are encountered in addition to amplitude death as the distance between the oscillators is varied. This study might be useful to understand synchronisation due to flame–flame interaction in modern multi-burner turbulent combustors where the constituent burners often have inherent dissimilarities. [ABSTRACT FROM AUTHOR]

In this paper we present a framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns, and oscillations that are invariant under the action of a finite-dimensional set of continuous isometries (such as translation or rotation). This formalism can accommodate patterns, waves, and oscillations in reaction-diffusion systems and neural field equations. To do this, we define the phase by precisely projecting the infinite-dimensional system onto the manifold of isometries. We outline a precise stochastic differential equation for the phase. The phase is then used to show that the probability of the system leaving the attracting basin of the manifold after an exponentially long period of time (in ε -2, the magnitude of the noise) is exponentially unlikely. [ABSTRACT FROM AUTHOR]

Many time series are considered to be a superposition of several oscillation components.We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship. [ABSTRACT FROM AUTHOR]

Paranormal believers' thinking is frequently biased by intuitive beliefs. Lack of inhibition of these tempting beliefs is considered a key element in paranormal believers' thinking. However, the brain activity related to inhibitory control in paranormal believers is poorly understood. We examined EEG activities at resting state in alpha, beta, and gamma bands with inhibitory control in paranormal believers and skeptics. The present study shows that paranormal belief is related to the reduced power of the alpha, beta, and gamma frequency bands, and reduced inhibitory control. This study may contribute to understanding the differences between believers and skeptics in brain activity related to inhibitory control in paranormal believers. [ABSTRACT FROM AUTHOR]

The need to estimate the delay times between elements of coupled oscillatory ensembles is frequently encountered in the analysis of systems of various natures, for which only separate records (time series) of the observed oscillations are available. The possibility of obtaining these estimates in the case of relatively short time series recorded in the presence of noise is considered. Using the well-known point estimator based on a model of the phase dynamics, an interval estimator is proposed, a correction that eliminates a bias of the point estimate is introduced, and a formula for the confidence interval is derived based on the maximum likelihood formalism. Possibilities of the proposed approach are illustrated by the results of numerical experiments in systems of coupled oscillators. [ABSTRACT FROM AUTHOR]

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With the growing demand for wearable computers, there is a need for material systems that can perform computational tasks without relying on external electrical power. Using theory and simulation, we design a material system that “computes” by integrating the inherent behavior of self-oscillating gels undergoing the Belousov–Zhabotinsky (BZ) reaction and piezoelectric (PZ) plates. These “BZ-PZ” units are connected electrically to form a coupled oscillator network, which displays specific modes of synchronization. We exploit this attribute in employing multiple BZ-PZ networks to perform pattern matching on complex multi-dimensional data, such as colored images. By decomposing a colored image into sets of binary vectors, we use each BZ-PZ network, or “channel,” to store distinct information about the color and the shape of the image and perform the pattern matching operation. Our simulation results indicate that the multi-channel BZ-PZ device can detect subtle differences between the input and stored patterns, such as the color variation of one pixel or a small change in the shape of an object. To demonstrate a practical application, we utilize our system to process a colored Quick Response code and show its potential in cryptography and steganography. [ABSTRACT FROM AUTHOR]

Conventional and modern methods for beam steering in antennas and radar systems have one goal in common: to manipulate the phase shift between oscillating components, so that the direction of a radiating intensity pattern can be controlled. Typical components include arrays of nonlinear oscillators connected in a chain configuration. Modern methods for beam steering take advantage of the inherent nonlinearities of the individual components and of the collective dynamics of the array of oscillators to successfully manipulate phase shift. None of those methods include, however, signal amplification. In this manuscript, we introduce a novel array configuration: a feedforward network, which allows, simultaneously, for beam steering and signal amplification capabilities. We show that the amplitudes of certain bifurcating solutions in a feedforward network of nonlinear oscillators exhibit growth rates that are significantly larger than in other type of networks that operate near the onset of a Hopf bifurcation. Those branches of oscillations have the potential to lead to significant signal amplification of a radiating beam. [ABSTRACT FROM AUTHOR]

We analyze the features of the oscillations arising in forced inductor-capacitor (LC) oscillators when they operate in the periodic pulling mode, under the action of a weak injection signal. In radio frequency integrated circuits, both voltage-controlled oscillators subject to undesired couplings and injection-locked frequency dividers behave like forced LC oscillators. These are modeled as second-order driven oscillators working in the subharmonic (secondary) resonance regime. The analysis is based on the generalized Adler's equation, which we introduce to describe the phase dynamics of dividers of any division ratio and to derive closed-form expressions for the spectrum components of the system's oscillatory response. We show that the spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance. Numerical and experimental results are given to validate the presented results, which significantly generalize those available in the literature. [ABSTRACT FROM AUTHOR]

The recent introduction of chronotaxic systems provides the means to describe nonautonomous systems with stable yet time-varying frequencies which are resistant to continuous external perturbations. This approach facilitates realistic characterization of the oscillations observed in living systems, including the observation of transitions in dynamics which were not considered previously. The novelty of this approach necessitated the development of a new set of methods for the inference of the dynamics and interactions present in chronotaxic systems. These methods, based on Bayesian inference and detrended fluctuation analysis, can identify chronotaxicity in phase dynamics extracted from a single time series. Here, they are applied to numerical examples and real experimental electroencephalogram (EEG) data. We also review the current methods, including their assumptions and limitations, elaborate on their implementation, and discuss future perspectives. [ABSTRACT FROM AUTHOR]

A model-based robust control approach is proposed that significantly improves imaging bandwidth for the dynamic mode atomic force microscopy. A model for cantilever oscillation amplitude and phase dynamics is derived and used for the control design. In particular, the control design is based on a linearized model and robust H∞ control theory. This design yields a significant improvement when compared to the conventional proportional-integral designs and verified by experiments. [ABSTRACT FROM AUTHOR]

There is growing interest in developing training programs to mitigate cognitive decline associated with normal aging. Here, we assessed the effect of 3‐month music and visual art training programs on the oscillatory brain activity of older adults using a partially randomized intervention design. High‐density electroencephalography (EEG) was measured during the pre‐ and post‐training sessions while participants completed a visual GoNoGo task. Time‐frequency representations were calculated in regions of interest encompassing the visual, parietal, and prefrontal cortices. Before training, NoGo trials generated greater theta power than Go trials from 300 to 500 ms post‐stimulus in mid‐central and frontal brain areas. Theta power indexing response suppression was significantly reduced after music training. There was no significant difference between pre‐ and post‐test for the visual art or the control group. The effect of music training on theta power indexing response suppression was associated with reduced functional connectivity between prefrontal, visual, and auditory regions. These results suggest that theta power indexes executive control mechanisms in older adults. Music training affects theta power and functional connectivity associated with response suppression. These findings contribute to a better understanding of inhibitory control ability in older adults and the neuroplastic effects of music interventions. [ABSTRACT FROM AUTHOR]

Brain oscillations emerge during sensory and cognitive processes and have been classified into different frequency bands. Yet, even within the same frequency band and between nearby brain locations, the exact frequencies of brain oscillations can differ. These frequency differences (detuning) have been largely ignored and play little role in current functional theories of brain oscillations. This contrasts with the crucial role that detuning plays in synchronization theory, as originally derived in physical systems. Here, we propose that detuning is equally important to understand synchronization in biological systems. Detuning is a critical control parameter in synchronization, which is not only important in shaping phase-locking, but also in establishing preferred phase relations between oscillators. We review recent evidence that frequency differences between brain locations are ubiquitous and essential in shaping temporal neural coordination. With the rise of powerful experimental techniques to probe brain oscillations, the contributions of exact frequency and detuning across neural circuits will become increasingly clear and will play a key part in developing a new understanding of the role of oscillations in brain function. [ABSTRACT FROM AUTHOR]

Rotating waves are a common occurrence in large scale recordings of brain oscillations. We examine the existence, stability, and form of rigid rotating waves in a nonlocally coupled phase model on the annulus. For odd interaction functions, it is possible to write down an explicit solution. When interactions are more general, we prove existence of the waves and use perturbation theory to estimate the shape, frequency, and stability of the waves. For large holes, we show that the phase satisfies a Burgers-type equation. We show that as the hole in the annulus decreases, the waves lose stability. Through numerical simulations, we suggest that the bifurcation that occurs with the shrinking hole is a saddle-node infinite cycle and gives rise to so-called spiral chimeras. [ABSTRACT FROM AUTHOR]

Neural oscillations provide a means for efficient and flexible communication among different brain areas. Understanding the mechanisms of the generation of brain oscillations is crucial to determine principles of communication and information transfer in the brain circuits. It is well known that the inhibitory neurons play a major role in the generation of oscillations in the gamma range, in pure inhibitory networks, or in the networks composed of excitatory and inhibitory neurons. In this study, we explore the impact of different parameters and, in particular, the delay in the transmission of the signals between the neurons, on the dynamics of inhibitory networks. We show that increasing delay in a reasonable range increases the synchrony and stabilizes the oscillations. Unstable gamma oscillations characterized by a highly variable amplitude of oscillations can be observed in an intermediate range of delays. We show that in this range of delays, other experimentally observed phenomena such as sparse firing, variable amplitude and period, and the correlation between the instantaneous amplitude and period could be observed. The results broaden our understanding of the mechanism of the generation of the gamma oscillations in the inhibitory networks, known as the ING (interneuron-gamma) mechanism. [ABSTRACT FROM AUTHOR]

Neural oscillations are ubiquitous across recording methodologies and species, broadly associated with cognitive tasks, and amenable to computational modelling that investigates neural circuit generating mechanisms and neural population dynamics. Because of this, neural oscillations offer an exciting potential opportunity for linking theory, physiology and mechanisms of cognition. However, despite their prevalence, there are many concerns—new and old—about how our analysis assumptions are violated by known properties of field potential data. For investigations of neural oscillations to be properly interpreted, and ultimately developed into mechanistic theories, it is necessary to carefully consider the underlying assumptions of the methods we employ. Here, we discuss seven methodological considerations for analysing neural oscillations. The considerations are to (1) verify the presence of oscillations, as they may be absent; (2) validate oscillation band definitions, to address variable peak frequencies; (3) account for concurrent non‐oscillatory aperiodic activity, which might otherwise confound measures; measure and account for (4) temporal variability and (5) waveform shape of neural oscillations, which are often bursty and/or nonsinusoidal, potentially leading to spurious results; (6) separate spatially overlapping rhythms, which may interfere with each other; and (7) consider the required signal‐to‐noise ratio for obtaining reliable estimates. For each topic, we provide relevant examples, demonstrate potential errors of interpretation, and offer suggestions to address these issues. We primarily focus on univariate measures, such as power and phase estimates, though we discuss how these issues can propagate to multivariate measures. These considerations and recommendations offer a helpful guide for measuring and interpreting neural oscillations. [ABSTRACT FROM AUTHOR]

A two-dimensional stabilized space-time finite-element-based in-house solver is used to explore flow around an elastically mounted rigid diamond oscillator undergoing undamped vortex-induced vibrations in transverse and stream-wise directions simultaneously. The computations are carried over a reduced velocity ( U * ) range of 1–12 keeping the Reynolds number (Re) and the mass ratio ( m * ) fixed at 100 and 10, respectively. In the current investigation, a five-branch response behavior with the presence of an "upper branch" is identified, which is absent for transverse-only oscillations. A shift in normalized time-averaged phase difference (ϕ / π) from 0 to 1 is related to the transition from the upper to the lower branch. The non-dimensional oscillation frequencies in both streamwise and cross-stream directions (Fx and Fy, respectively) collapse on the upper branch, matching the oscillator's non-dimensional natural frequency (FN). This leads to periodic single-looped "raindrop-shaped" cylinder trajectories. On this branch, the vortex-shedding mode is asymmetric, and the mean lift is non-zero ( C l avg ≠ 0). For all other response branches, C l avg ≈ 0 and the vortex-shedding modes are symmetric. The presence of multiple frequencies in the in-line oscillations makes the initial branch quasi-periodic, whereas all other response branches are periodic. The addition of in-line motion modifies the fluid loading on the oscillator significantly. [ABSTRACT FROM AUTHOR]

High-stability optoelectronic oscillators (OEOs) are attained using self-forced oscillation techniques using long optical delays. Free-running InP-based multi-mode laser (MML) diodes with free-spectral range (FSR) of 11.7 GHz is stabilized using self-electrical injection-locked (SEIL) and dual self-phase-locked loop (DSPLL) (SEILDPLL) approach; phase noise of the free-running OEO of −52.8 dBc/Hz at 10-kHz offset was improved by 36 dB experimentally. Self-forced stabilization of MML-based OEO results in timing jitter of 0.9 ps, a factor of 33 times reduction in the free-running performance. A fully integrated solution using Si-photonics (SiP) is more environmentally stable and amenable to a reduced large volume manufacturing. A heterogeneously integrated MML combined with self-forced function is designed on an approximately 91-cm2 SiP chip using 325- and 975-ns time delays. [ABSTRACT FROM AUTHOR]

Different cortical dynamics of alpha oscillations (8-13Hz) have been associated with increasedworkingmemory load,which have been mostly interpreted as a neural correlate of functional inhibition. This study aims at determining whether different manifestations of load-dependent amplitude and phase dynamics in the alpha band can coexist over different cortical regions. To address this question, we increased information load by manipulating the number and spatial configuration of domino spots. Time--frequency analysis of EEG source activity revealed (i) load-independent increases of both alpha power and interregional alpha-phase synchrony within task-irrelevant, posterior cortical regions and (ii) load-dependent decreases of alpha power over areas of the left pFC and bilateral posterior parietal cortex (PPC) preceded in time by load-dependent decreases of alpha-phase synchrony between the left pFC and the left PPC. The former results support the role of alpha oscillations in inhibiting irrelevant sensorimotor processing, whereas the latter likely reflect release of parietal task-relevant areas from top--down inhibition with load increase. This interpretation found further support in a significant latency shift of 15 msec from pFC to the PPC. Together, these results suggest that amplitude and phase alpha dynamics in both local and long-range cortical networks reflect different neural mechanisms of top--down control thatmight be crucial inmediating the different working memory processes. [ABSTRACT FROM AUTHOR]

Early excited state dynamics in the photodissociation of transition metal carbonyls determines the chemical nature of short-lived catalytically active reaction intermediates. However, time-resolved experiments have not yet revealed mechanistic details in the sub-picosecond regime. Hence, in this study the photoexcitation of ironpentacarbonyl Fe(CO)5 is simulated with semi-classical excited state molecular dynamics. We find that the bright metal-to-ligand charge-transfer (MLCT) transition induces synchronous Fe-C oscillations in the trigonal bipyramidal complex leading to periodically reoccurring release of predominantly axial CO. Metaphorically the photoactivated Fe(CO)5 acts as a CO geyser, as a result of dynamics in the potential energy landscape of the axial Fe-C distances and non-adiabatic transitions between manifolds of bound MLCT and dissociative metal-centered (MC) excited states. The predominant release of axial CO ligands and delayed release of equatorial CO ligands are explained in a unified mechanism based on the σ*(Fe-C) anti-bonding character of the receiving orbital in the dissociative MC states. The photodissociation of transition metal carbonyls is involved in catalysis and synthetic processes. Here the authors, using semi-classical excited state molecular dynamics, observe details of the early stage dynamics in the photodissociation of Fe(CO)5, including synchronous bursts of CO at periodic intervals of 90 femtoseconds. [ABSTRACT FROM AUTHOR]

In this paper, we present a study of a simplified optoelectronic oscillator (OEO) that features both the laser and the filter nonlinearities. We show that this optoelectronic oscillator depicts the phenomena of quasi-sinusoidal oscillations when the feedback gain is small, relaxation and chaos oscillations when the feedback gain increases. It is analytically confirmed that the frequencies of the limit-cycle oscillations increase with the cubic-nonlinear term and the feedback gain but decrease with the time-delay of the system. The experimental measurements are qualitatively in agreement with the theoretical and numerical analysis. [ABSTRACT FROM AUTHOR]

Specific frequency bands of neural oscillations have been correlated with a range of cognitive and behavioral effects (e.g., memory and attention). The causal role of specific frequencies may be investigated using transcranial alternating current stimulation (tACS), a non-invasive brain stimulation method. TACS involves applying a sinusoidal current between two or more electrodes attached on the scalp, above neural regions that are implicated in cognitive processes of interest. The theorized mechanisms by which tACS affects neural oscillations have implications for the exact stimulation frequency used, as well as its anticipated effects. This review outlines two main mechanisms that are thought to underlie tACS effects – entrainment, and spike-timing dependent plasticity (STDP). Entrainment suggests that the stimulated frequency synchronizes the ongoing neural oscillations, and is thought to be most effective when the stimulated frequency is at or close to the endogenous frequency of the targeted neural network. STDP suggests that stimulation leads to synaptic changes based on the timing of neuronal firing in the target neural network. According to the principles of STDP, synaptic strength is thought to increase when pre-synaptic events occur prior to post-synaptic events (referred to as long-term potentiation, LTP). Conversely, when post-synaptic events occur prior to pre-synaptic events, synapses are thought to be weakened (referred to as long-term depression, LTD). In this review, we summarize the theoretical frameworks and critically review the tACS evidence for each hypothesis. We also discuss whether each mechanism alone can account for tACS effects or whether a combined account is necessary. [ABSTRACT FROM AUTHOR]