Search

The change in the phase, from quiescence to surge, may perturb the glacier’s dynamical behavior. To understand these changes through geospatial technique, the fastest moving tidewater Monacobreen Glacier, Svalbard, was studied for the year 2016–2019. It was elucidated that the surge had initiated during 2017–2018 before it the glacier was in quiescence since 2001. Initially, the glacier radar zones, namely percolation refreeze, lower percolation, and clean ice, were identified using the multi-temporal SAR data. These zones were utilized to delineate the equilibrium line altitude, and it was found that it is continuously moving down during surging, unlike the quiescence phase. The accumulation area ratio was always more than 0.67 throughout the analysis. The seasonal change in glacier surface velocity for both the phases was estimated, adapting the most appropriate Offset Tracking approach using the SAR data. The mean velocity over the main trunk was found to vary from 0.5 to 4 m/day. Thereafter, Glen's flow law equation was used to estimate the ice-thickness and found that the glacier has an average thickness range of 216–326 m in quiescence and 136–244 m during the surging. The analysis depicted that the basal shear stresses are increasing with surging, and the viscosity is decreasing. It can be said that the transition of the glacier from quiescent to surging phase has entirely changed its dynamic behavior and characteristics. Further, in the absence of field observations, the geospatial technique may provide reasonable estimates of the glacier’s physical and dynamical parameters.

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

The phase of low-frequency, rhythmic cortical activity is essential for organizing brain processes because it provides a recurrent temporal frame for information coding. However, the low-frequency cortical phase exhibits great flexibility in response to external influences. Given that brain rhythms have been found to track respiratory inputs, we hypothesized that slow breathing, commonly associated with mental regulation, could reorganize the relationship between these two rhythmic systems through the adjustment of the cortical phase to such a slow train of inputs. Based on simultaneous magnetoencephalography and respiratory measurements, we report that while participants performed paced breathing, slow relative to normal breathing modulated cortical phase activity in the alpha range across widespread brain areas. Such modulation effects were specifically locked to the middle of the inspiration stage and exhibited a well-structured pattern. At the single-subject level, the phase angles underlying the effects became more likely to be diametrically opposed across breaths, indicating unique and consistent phase adjustment to slow inspiratory inputs. Neither cardiac fluctuations nor breathing-unrelated task effects could account for the findings. We suggest that slow-paced inspiration could organize the cortical phase in a regularized phase pattern, revealing a rhythmic but dynamic neural network integrated with different neurophysiological systems through volitional control. NEW & NOTEWORTHY Breathing is more complicated than a simple gas exchange, as it is integrated with numerous cognitive and emotional functions. Controlled slow breathing has often been used to regulate mental processes. This magnetoencephalography study demonstrates that slow-paced relative to normal-paced inspiration could organize the timing of alpha rhythmic activities across breathing cycles in a structured manner over widespread brain areas. Our results reveal how a volitionally controlled change in respiratory behavior could systematically modulate cortical activity.

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

Intrinsic optical signal (IOS) imaging promises a noninvasive method for objective assessment of retinal function. This study demonstrates concurrent optical coherence tomography (OCT) of amplitude-IOS and phase-IOS changes in human photoreceptors. A new procedure for differential-phase-mapping (DPM) is validated to enable depth-resolved phase-IOS imaging. Dynamic OCT revealed rapid amplitude-IOS and phase-IOS changes, which occur almost right away after the stimulus onset. These IOS changes were predominantly observed within the photoreceptor outer segment (OS), particularly two boundaries connecting to the inner segment and retinal pigment epithelium. The comparative analysis supports that both amplitude-IOS and phase-IOS attribute to transient OS morphological change associated with phototransduction activation in retinal photoreceptors. A simulation modeling is proposed to discuss the relationship between the photoreceptor OS length and phase-IOS changes.

The authors show that neural networks exhibiting noise-induced rhythms, also known as quasi-cycle oscillations, can synchronize through out-of-phase locking depending on the noise intensity and the size of the coupling delay

When a solute molecule is placed in solution, is it acceptable to presume that its electronic structure is essentially the same as that in the gas phase? In this paper, we address this question from a simulation perspective for the case of the sodium dimer cation (Na

Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. We demonstrate experimentally the appearance of giant fractional Shapiro steps in anisotropic Josephson junction arrays as unambiguous evidence of a skewed current phase relationship. Introducing anisotropy in the array results in a giant collective high frequency response that reflects the properties of a single junction, as evidenced by the observation of a Fraunhofer like magnetic field dependence of the total critical current of the system. The observed phase dynamics can be perfectly captured within an extended resistively shunted Josephson junction model. These results directly indicate the potential of Josephson junction arrays to explore the current phase relation in a very broad frequency range (down to 50 MHz) and in a wide variety of novel link materials exhibiting non-conventional current phase relationships. Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. Here, the authors demonstrate the observation of giant fractional Shapiro steps in an anisotropic Josephson junction array, as unambiguous evidence of a skewed current phase relationship.

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both.

Previous research has shown that feedback evaluation is sensitive to monetary incentive. We investigated whether this sensitivity is driven by motivational salience (the difference between both rewarding and punishing events versus neutral events) or by motivational valence (the difference between rewarding and punishing events). Fifty-seven participants performed a monetary incentive delay task under a gain context, a loss context, and a neutral context with their electroencephalogram recorded. During the time domain, the feedback-related negativity (FRN) showed a motivational salience effect whereas the P3 displayed a reward valence effect. During the time-frequency domain, we observed a motivational salience effect for phase-locked theta power regardless of performance feedback, but a reward valence effect for non-phase-locked theta power in response to unsuccessful feedback. Moreover, we found a reward valence effect for phase-locked delta. These findings thus suggest that the affective modulation on feedback evaluation can be driven either by motivational valence or by motivational salience, which depends on the temporal dynamics (the FRN vs. the P3), the frequency dynamics (theta vs. delta power), as well as the phase dynamics (evoked vs. induced power).

Although Mn-Ga alloys are discussed as novel permanent magnetic materials, there are several drawbacks, including the high price of Ga and the yet too small saturation magnetization to name a few. We used several guidelines to motivate the replacement of Ga by Sn to tackle these issues and explored the phase formation, structural and magnetic properties of a Mn 2.6 Ga 1− x Sn x alloy series. The structure of Sn-rich samples is dominated by the corresponding hexagonal and orthorhombic phases, while the structure of Ga-rich samples shows additional contributions from the tetragonal DO 22 structure. However, formation of the tetragonal phase happens only upon an appropriate annealing procedure. In contrast to the discussion in the literature, our experiments do not hint on the tetragonal DO 22 structure being metastable, but rather indicate the DO 22 structure being an equilibrium phase. In general, the experimentally found phase fractions impact on the magnetic properties and hard magnetic properties are downgraded very rapidly even if only a small amount of Ga is substituted by Sn. This indicates that the DO 22 phase found only in the Ga-rich samples is indeed the one which is most relevant for realization of high magnetic anisotropy.

Objective:We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.Material and Methods:In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.Results:Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.Conclusion:Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

Under consideration is the system of partial differential equations describing the dynamics of a two-phase medium. Exact partially invariant solutions of rank 1 and defect 1 of this system are obtained with respect to some four-dimensional subalgebras. The phenomenon of collapse (an instantaneous source) in a two-phase medium is described.

We study a model of fatigue accumulation in an oscillating elastoplastic beam under the hypothesis that the material can partially recover by the effect of melting. The model is based on the idea that the fatigue accumulation is proportional to the dissipated energy. We prove that the system consisting of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics admits a unique strong solution.

We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart–Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation procedure to explicitly obtain the higher-order approximation. We demonstrate this by deriving the second-order phase equations for a network of three Stuart–Landau oscillators. For systems where explicit expressions of the phase are not available, we present a numerical procedure that constructs the phase dynamics equations for a small network of coupled units. We apply this approach to a network of three van der Pol oscillators and reveal components in the coupling with different scaling in the interaction strength.

Josephson junctions with weak-links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. Further, such devices offer a direct probe of novel material properties, for example in the search for Majorana fermions. In this work, we report on DC and AC Josephson effect of high-mobility, hexagonal boron nitride (h-BN) encapsulated graphene Josephson junctions. On the application of RF radiation, we measure phase-locked Shapiro steps. An unexpected bistability between $\pm 1$ steps is observed with switching times on the order of seconds. A critical scaling of a bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This work draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.

Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency-multi-clusters by investigating the effect of the time-scale separation. We show that the slow adaptation in comparison with the fast phase dynamics is necessary for the emergence of the multi-clusters and their stability. Additionally, we study the role of double antipodal clusters, which appear to be unstable for all considered parameter values. We show that such states can be observed for a relatively long time, i.e., they are metastable. A geometrical explanation for such an effect is based on the emergence of a heteroclinic orbit., 16 pages, 8 figures

First order phase reduced model is a good approximation of the dynamics of forced nonlinear oscillators near its limit cycle. The phase evolution is determined by the unforced frequency, the forcing term, and the phase response curve (PRC). Such models arise in biological oscillations such as in circadian rhythm, neural signaling, heart beat, etc. This technical note focuses on the phase regulation of the circadian rhythm using light intensity as the input. Though the model is simple, the circle topology of the state space needs to be carefully addressed. The most common entrainment method is to use a periodic input, such as in our daily light-dark cycle. We obtain the complete stable entrainment condition based on the entraiment input and the PRC. Motivated by the jet-lag problem, we also consider the minimum time entrainment control to achieve a specified phase shift. Application of the Pontryagin Minimum Principle leads to an efficient solution strategy for the optimal control, without solving the two-point boundary value problem. The optimal control may be further represented as a feedback control law based on the current and desired phases. Our analysis allows the answer to questions such as: When traveling from New York to Paris, is it faster to use light to shift the phase forward by 6 hours or delay the phase by 18 hours? The answer is somewhat counter-intuitive—delaying by 18 hours requires less time. The general answer depends on the light intensity level and the shape of the PRC. PRCs for human and Drosophila from the literature are used to illustrate the results.

In this work, a Lattice-Boltzmann-Method (LBM) model for simulating hysteresis in a proton exchange membrane (PEMFC) electrode is presented. One of the main challenges hindering study of the cathode catalyst layer (CCL) in PEMFCs is the lack of understanding of two-phase transport and how it affects electrochemical performance. Researchers have typically used high level approximations that oversimplify the microstructure of the CCL—these are known as macrohomogenous models. However, as the field has progressed, the flaws in these idealizations are being revealed, especially in areas of improving our understanding of flooding as well as catalyst layer hysteresis. Previously, the microstructure details needed to build an accurate mesoscale model have eluded researchers; however, with advances in tomography and focused-ion-beam scanning-electron-microscopy (FIB-SEM), creating these representations has become possible. Using LBM with these representations, the difficult problem of catalyst layer capillary hysteresis can be examined. In two-phase capillary hysteresis, both the equilibrium saturation position as well as absolute value depends on the wetting history. Based on the models, it is ascertained that at lower capillary numbers, the liquid begins to undergo capillary fingering – only above a capillary pressure of 5 MPa, a regime change into stable displacement is observed. As capillary fingering does not lead to uniform removal of liquid, the prediction is that because high capillary pressures are needed to change to the regime of stable displacement, wicking will not be an effective means of water removal. Figure 1

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking., Comment: 10 pages, 8 figures

Small-signal stability assessment of the three-phase system can be performed using the measured impedances of the load and source. To obtain the dc steady-state operation point, the impedances are measured in the rotating $\boldsymbol{dq}$ -frame, and the phase angle is needed for the coordinate transformation used in both the perturbation injection and the impedance calculation. However, the phase estimation may introduce additional dynamics, affecting the accuracy of impedance measurement. This paper investigates the impact of phase synchronization dynamics on the measured impedance results. It is revealed that the phase variations in the perturbation injection has little effect on the measured impedance, while the phase dynamics introduced in the impedance calculation may have a significant impact. Based on impedance transformation, a new impedance calculation method is proposed, which can reduce the errors caused by the phase dynamics. Finally, the simulation and experiment results verify the accuracy of the analytical results and the effectiveness of the proposed method.

Sensorimotor predictions are essential for adaptive behavior. In natural environments, events that demand sensorimotor predictions unfold across many timescales, and corresponding temporal predictions (either explicit or implicit) should therefore emerge in brain dynamics. Neuronal oscillations are scale-specific processes found in several frequency bands. They underlie periodicity in sensorimotor processing and can represent temporal predictions via their phase dynamics. These processes build upon endogenous neural rhythmicity and adapt in response to exogenous timing demands. While much of the research on periodicity in neural processing has focused on subsecond oscillations, these fast-scale rhythms are in fact paralleled by critical-like, scale-free dynamics and fluctuations of brain activity at various timescales, ranging from seconds to hundreds of seconds. In this review, we put forth a framework positing that critical brain dynamics are essential for the role of neuronal oscillations in timing and that cross-frequency coupling flexibly organizes neuronal processing across multiple frequencies.

While Boolean logic has been the backbone of digital information processing, there exist classes of computationally hard problems wherein this paradigm is fundamentally inefficient. Vertex coloring of graphs, belonging to the class of combinatorial optimization, represents one such problem. It is well studied for its applications in data sciences, life sciences, social sciences and technology, and hence, motivates alternate, more efficient non-Boolean pathways towards its solution. Here we demonstrate a coupled relaxation oscillator based dynamical system that exploits insulator-metal transition in Vanadium Dioxide (VO

In multi-modular process architectures with independent but interacting subsystems, identification may not be the first choice at hand for closed loop control. A robust relay-based PID autotuning strategy is presented and validated on a quadruple tank system with non-minimum phase dynamics. The controller ensures a specified closed loop robustness, which is of great benefit to the overall performance. The experimental results suggest that the proposed method fulfils the robustness requirement and performs well in various operating conditions of the testbench.

Tomography is a non-invasive, non-intrusive imaging technique allowing the visualization of phase dynamics in industrial and biological processes. This article reviews progress in Electrical Capacitance Volume Tomography (ECVT). ECVT is a direct 3D visualizing technique, unlike three-dimensional imaging, which is based on stacking 2D images to obtain an interpolated 3D image. ECVT has recently matured for real time, non-invasive 3-D monitoring of processes involving materials with strong contrast in dielectric permittivity. In this article, ECVT sensor design, optimization and performance of various sensors seen in literature are summarized. Qualitative Analysis of ECVT image reconstruction techniques has also been presented.

We examine the impact of small parity-time () symmetric perturbations on nonlinear optical honeycomb lattices in the tight-binding limit. We show for strained lattices that complex dispersion relationships do not form under perturbation, and we find a variety of nonlinear wave equations which describe the effective dynamics in this regime. The existence of semilocalized gap solitons in this case is also shown, though we numerically demonstrate these solitons are likely unstable. We show for unstrained lattices under the effect of a restricted class of perturbations, which prevent complex dispersion relationships from appearing, that nontrivial phase dynamics emerge as a result of the perturbation. This phase can be understood as momentum imparted to optical beams by the lattice, thus showing perturbations offer potentially novel means for the control of light in honeycomb lattices.

Rider models are employed to gain insight into bicycle rider steering behaviour and to improve characteristic properties of bicycles. In this paper, stability properties as well as basic dynamic characteristics of the passive (uncontrolled) bicycle-rider system and consequences on the rider control modelling are addressed. In particular, the unstable motion of the system at low velocities and bandwidth limitations caused by non-minimum phase dynamics are emphasized. To analyse the effectiveness of the steering torque and the lean torque as possible rider's inputs to control the dynamics of the bicycle, a controllability analysis of the bicycle-rider system has been performed. It turns out that lean torque input, in contrast to steering torque input, has marginal impact on the dynamics of the system. Finally, a bicycle rider control model considering human rider properties is presented, and its capabilities are demonstrated by performing a curve entering manoeuvre.

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact., Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. The collective phase sensitivity and collective phase coupling functions, which quantitatively characterize the macroscopic rhythms, are illustrated using three representative models of limit-cycle oscillators. As an important result of the theory, we demonstrate noise-induced anti-phase synchronization between macroscopic rhythms by direct numerical simulations of the three models., Comment: 19 pages, 11 figures

A minimal model of nonlinear phase dynamics in drift waves is shown to support phase bore solutions. Coupled nonlinear equations for amplitude, phase, and zonal flow are derived for the Hasegawa-Mima system and specialized to the case of spatiotemporally constant amplitude. In that limit, phase curvature (finite second derivative of the phase with respect to the radius) alone generates propagating shear flows. The phase field evolves nonlinearly by a competition between phase steepening and dispersion. The analytical solution of the model reveals that the phase bore solutions so obtained realize the concept of a phase slip in a concrete dynamical model of drift wave dynamics. The implications for phase turbulence are discussed.

Neural oscillatory dynamics are a candidate mechanism to steer perception of time and temporal rate change. While oscillator models of time perception are strongly supported by behavioral evidence, a direct link to neural oscillations and oscillatory entrainment has not yet been provided. In addition, it has thus far remained unaddressed how context-induced illusory percepts of time are coded for in oscillator models of time perception. To investigate these questions, we used magnetoencephalography and examined the neural oscillatory dynamics that underpin pitch-induced illusory percepts of temporal rate change. Human participants listened to frequency-modulated sounds that varied over time in both modulation rate and pitch, and judged the direction of rate change (decrease vs increase). Our results demonstrate distinct neural mechanisms of rate perception: Modulation rate changes directly affected listeners' rate percept as well as the exact frequency of the neural oscillation. However, pitch-induced illusory rate changes were unrelated to the exact frequency of the neural responses. The rate change illusion was instead linked to changes in neural phase patterns, which allowed for single-trial decoding of percepts. That is, illusory underestimations or overestimations of perceived rate change were tightly coupled to increased intertrial phase coherence and changes in cerebro-acoustic phase lag. The results provide insight on how illusory percepts of time are coded for by neural oscillatory dynamics.

We consider networks of coupled phase oscillators of different complexity: Kuramoto–Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.