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The work is devoted to the application of various nonlinear dynamics methods to identify interactions in short noisy time series extracted from biological rhythms related to the respiratory, cardiovascular and nervous systems. These interactions are considered as transitions to synchronized states, as the coupling directionality and the delay time in the influence of one system on another. For the analyzed data, the relationship between these rhythms is due to the fact that the neurons of medulla are related to the brain response to changes in blood pressure and respiration during external pain stimulation. Phase synchronization between the variability of blood pressure and respiratory fluctuations in response to these stimuli was established in half of the analyzed time series using methods for assessing phase synchronization based on finding instantaneous phases by the synchrosqueezed wavelet transform and based on calculating the recurrences of phase trajectories. For unsynchronized time series, a predominantly unidirectional influence of respiratory rhythm fluctuations on the blood pressure variability was obtained by the method of phase dynamics modeling and the method of estimating recurrence probabilities. For two third of the data, a unidirectional influence of the blood pressure variability on the neuronal variability was determined, and the remaining data were characterized by a bidirectional relationship between the neuronal and blood pressure variability. Delay time estimation by phase dynamics modeling showed reduced time of influence of the blood pressure variability on the neuronal variability in bidirectional coupling compared to the influence of the neuronal variability on the blood pressure variability. [ABSTRACT FROM AUTHOR]

In this study, a numerical analysis is carried out to investigate the coupled behaviour of a TLP (tension leg platform) -TAD (tender-assisted drilling) system under a series of regular waves in surge direction. The numerical model is established in the time domain considering the nonlinear characteristics of the mooring systems and the hydrodynamic interference. After the case validations, the effects of the wave periods and amplitudes on the nonlinear dynamic characteristics of the surge motions are investigated in detail. Then, the observed nonlinear dynamic characteristics are interpreted in detail through the existing theory of phase dynamics. The surge motions of the coupled system can show multiperiod nonlinear characteristics under regular waves in certain wave periods. Three forms of phase dynamic characteristics: phase locking, phase trapping, and phase drifting and slipping are observed in the surge motions of the tender-assisted drilling operation system. [ABSTRACT FROM AUTHOR]

Characterizing the brain's dynamic pattern of response to an input in electroencephalography (EEG) is not a trivial task due to the entanglement of the complex spontaneous brain activity. In this context, the brain's response can be defined as (1) the additional neural activity components generated after the input or (2) the changes in the ongoing spontaneous activities induced by the input. Moreover, the response can be manifested in multiple features. Three commonly studied examples of features are (1) transient temporal waveform, (2) time–frequency representation, and (3) phase dynamics. The most extensively used method of average event-related potentials (ERPs) captures the first one, while the latter two and other more complex features are attracting increasing attention. However, there has not been much work providing a systematic illustration and guidance for how to effectively exploit multifaceted features in neural cognitive research. Based on a visual oddball ERPs dataset with 200 participants, this work demonstrates how the information from the above-mentioned features are complementary to each other and how they can be integrated based on stereotypical neural-network-based machine learning approaches to better exploit neural dynamic information in basic and applied cognitive research. [ABSTRACT FROM AUTHOR]

The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations. [ABSTRACT FROM AUTHOR]

Circadian rhythms are internal processes repeating approximately every 24 hours in living organisms. The dominant circadian pacemaker is synchronized to the environmental light-dark cycle. Other circadian pacemakers, which can have noncanonical circadian mechanisms, are revealed by arousing stimuli, such as scheduled feeding, palatable meals and running wheel access, or methamphetamine administration. Organisms also have ultradian rhythms, which have periods shorter than circadian rhythms. However, the biological mechanism, origin, and functional significance of ultradian rhythms are not well-elucidated. The dominant circadian rhythm often masks ultradian rhythms; therefore, we disabled the canonical circadian clock of mice by knocking out Per1/2/3 genes, where Per1 and Per2 are essential components of the mammalian light-sensitive circadian mechanism. Furthermore, we recorded wheel-running activity every minute under constant darkness for 272 days. We then investigated rhythmic components in the absence of external influences, applying unique multiscale time-resolved methods to analyze the oscillatory dynamics with time-varying frequencies. We found four rhythmic components with periods of ∼17 h, ∼8 h, ∼4 h, and ∼20 min. When the ∼17-h rhythm was prominent, the ∼8-h rhythm was of low amplitude. This phenomenon occurred periodically approximately every 2-3 weeks. We found that the ∼4-h and ∼20-min rhythms were harmonics of the ∼8-h rhythm. Coupling analysis of the ridge-extracted instantaneous frequencies revealed strong and stable phase coupling from the slower oscillations (∼17, ∼8, and ∼4 h) to the faster oscillations (∼20 min), and weak and less stable phase coupling in the reverse direction and between the slower oscillations. Together, this study elucidated the relationship between the oscillators in the absence of the canonical circadian clock, which is critical for understanding their functional significance. These studies are essential as disruption of circadian rhythms contributes to diseases, such as cancer and obesity, as well as mood disorders. [ABSTRACT FROM AUTHOR]

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 respiratoryrelated 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. [ABSTRACT FROM AUTHOR]

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. [ABSTRACT FROM AUTHOR]

The dispersionless Whitham modulation equations in 2 + 1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2 + 1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. [ABSTRACT FROM AUTHOR]

A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems. [ABSTRACT FROM AUTHOR]

The phase dynamics of two phase wavetrains in the coupled non-linear Schrödinger (NLS) equations are investigated as an example of the dispersion arising from singular wave action. It is shown that when the wavetrain becomes singular, there is a reduction from coupled NLS to a scalar Korteweg–de Vries (KdV) equation, and if there is a further degeneracy the scalar two-way Boussinesq emerges. This is the first such derivation of the two-way Boussinesq reduction in this setting. A novelty in the theory is that the coefficients in the resulting equations are determined from properties of the wavetrain and underlying conservation laws. This theory generalizes the reduction from a single defocussing NLS equation to the KdV equation, and introduces Boussinesq dynamics to finite amplitude states in this family. A discussion of the effect of the phase dynamics on the wavetrain solution shows that the reductions provide an insight into a mechanism for the bifurcation of periodic wavetrains to dark and bright solitary waves. [ABSTRACT FROM AUTHOR]

Light is the primary signal that calibrates circadian neural circuits and thus coordinates daily physiological and behavioral rhythms with solar entrainment cues. Drosophila and mammalian circadian circuits consist of diverse populations of cellular oscillators that exhibit a wide range of dynamic light responses, periods, phases, and degrees of synchrony. How heterogeneous circadian circuits can generate robust physiological rhythms while remaining flexible enough to respond to synchronizing stimuli has long remained enigmatic. Cryptochrome is a short-wavelength photoreceptor that is endogenously expressed in approximately half of Drosophila circadian neurons. In a previous study, physiological light response was measured using real-time bioluminescence recordings in Drosophila whole-brain explants, which remain intrinsically light-sensitive. Here we apply analysis of real-time bioluminescence experimental data to show detailed dynamic ensemble representations of whole circadian circuit light entrainment at single neuron resolution. Organotypic whole-brain explants were either maintained in constant darkness (DD) for 6 days or exposed to a phase-advancing light pulse on the second day. We find that stronger circadian oscillators support robust overall circuit rhythmicity in DD, whereas weaker oscillators can be pushed toward transient desynchrony and damped amplitude to facilitate a new state of phase-shifted network synchrony. Additionally, we use mathematical modeling to examine how a network composed of distinct oscillator types can give rise to complex dynamic signatures in DD conditions and in response to simulated light pulses. Simulations suggest that complementary coupling mechanisms and a combination of strong and weak oscillators may enable a robust yet flexible circadian network that promotes both synchrony and entrainment. A more complete understanding of how the properties of oscillators and their signaling mechanisms facilitate their distinct roles in light entrainment may allow us to direct and augment the circadian system to speed recovery from jet lag, shift work, and seasonal affective disorder. [ABSTRACT FROM AUTHOR]

We systematically investigated precursory seismic patterns using the pattern informatics (PI) method and suggest an operable procedure for making PI maps for all seasons, in the context of earthquake forecasting. We examined the PI patterns before several inland earthquakes with magnitudes larger than 6, which occurred between 2001 and 2010 in Taiwan. We fixed a cutoff magnitude and a change interval, which is the time span used to calculate the seismicity change. Our results show that locations with high PI anomalies are typically associated with large earthquakes when the cutoff magnitude is 3.2 and the change interval is 4 years. Therefore, the PI method can be utilized as a routine forecasting tool with regular updates, such performing the PI calculation every season. We also conducted random tests, the results of which indicate a significant difference between large events and random, hypothetical events. [ABSTRACT FROM AUTHOR]

The effect of pumping methods on the gain and phase dynamics of quantum-dot vertical cavity semiconductor optical amplifier is investigated. The gain and phase recovery time is considered at the ground state transition wavelength. By including the effect of the excited state and wetting layer on the refractive index change, it is shown that under electrical pumping, the better gain dynamics is achieved compared to the optical pumping scheme. However, the phase recovery time can be accelerated by optical pumping. These behaviors result from the different mechanisms of population inversion in these two pumping methods. [ABSTRACT FROM PUBLISHER]

The moderately damped regime (MDR) in a Josephson junction (JJ) is quite distinct from the well-known case of underdamped systems and quite common in devices characterized by low critical currents. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics and the transport also in nontrivial cases of moderate damping. MDR is going to be more and more common with advances in nanopatterning superconductors and in materials science finalized to build hybrid devices. We report on measurements of SCDs, both in the thermal and quantum regime, on moderately damped NbN/MgO/NbN JJs. A transition from the Thermal Activation (TA) regime to Macroscopic Quantum Tunnelling (MQT) occurs at about 90 mK, while above 1.6 K a phase diffusive dynamics is clearly observed. The combined analysis of these regimes through numerical simulations allowed us to extract the fundamental parameters, which completely characterize the phase dynamics of such moderately damped JJs. [ABSTRACT FROM AUTHOR]

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit “flips” in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous—a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy. [ABSTRACT FROM AUTHOR]

Building on semiological research (i.e., the study of signs and symbols of all kinds) investigating the use of symbols in cinematic portrayals of travel behavior, this article describes a phase dynamics theory of epiphany travel behavior. Core propositions of the theory include (1) epiphany travel behavior and storytelling about such travel includes identifiable phases: prequel, awakening, journey, catharsis, and post-journey storytelling and reinterpreting; (2) world and personal blocks occur; (3) during the journey the protagonist recognizes the need for help and experiences help from key facilitators to reach desired physical locations and other goal objects; and (4) experiencing an archetypal force is an outcome of the journey. Such theory building provides a gestalt view and understanding of epiphany travel behavior. [ABSTRACT FROM AUTHOR]

By means of an electron hole rate equation model we explain the phase dynamics of a quantum dot semiconductor optical amplifier and the appearance of different decay times observed in pump and probe experiments. The ultrafast hole relaxation leads to a first ultrafast recovery of the gain, followed by electron relaxation and, in the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. We explain the ultrafast response of quantum dot amplifiers as an effect of hole escape and recombination without the need to assume Auger processes. [ABSTRACT FROM AUTHOR]

We study a learning and recalling model of phase patterns in a two- or three-coupled BVP oscillators system with a time delay δ. The coupling strengths are modulated by the Hebbian learning rule. Assuming the first-order approximation, we calculate the optimal condition of δ for exact recall by applying the phase dynamics theory. When α = 0, where α represents the coupling from activator to inhibitor, the correlation between the learning and the retrieval phase depends on δ. When α = 1, exact recall is achieved independent of δ. The results can be explained by the phase dynamics theory. [ABSTRACT FROM AUTHOR]

The purpose of this investigation was to use relative phase dynamics to evaluate gait in individuals with a reconstructed anterior cruciate ligament (ACL) during walking and running. Relative phase dynamics can describe the coordination strategies between the interacting segments at the lower extremity. Ten subjects who had undergone ACL reconstruction using the central third of their patellar tendon and ten healthy controls walked and ran on a treadmill at a self-selected pace. Relative phase dynamics were calculated for the foot-shank and shank-thigh coordinative relationships. Statistical differences between the groups were noted for the foot-shank relationship (p < 0.05) during both walking and running and for the shank-thigh relationship (p < 0.05) during walking. Our results indicate that current ACL reconstructive techniques may result in altered relative phase dynamics. These changes in relative phase dynamics could be related to a loss of sensory information about joint position and velocity that is typically provided by the intact ACL. Additionally, relative phase adaptations could be a learned response from the early stages of postsurgical rehabilitation. Relative phase dynamics provide quantitative information about the dynamic status of the ACL-reconstructed knee that cannot be gained from the conventional time-series evaluation of gait analysis data. Relative phase dynamics measures should supplement the conventional gait analysis measures that are used today for the clinical evaluation of the functional dynamic stability of the reconstructed knee. The examination of relative phase dynamics could be clinically important for the quantification of new ACL surgical interventions and of patient performance at various stages of rehabilitation. Further research should incorporate relative phase dynamics to understand the influence of ACL reconstruction on coordination and functional patient outcomes. [ABSTRACT FROM AUTHOR]

We describe the phase dynamics of a timing extraction system based on direct optical injection locking of a multifrequency oscillator employing an InGaAs/InP heterojunction bipolar phototransistor. We present a general model for the locking range, jitter transfer function, and output phase noise. The model is confirmed by a series of locking experiments. We consider first fundamental timing extraction, that is, a 10-GHz oscillator extracting the clock from a 10-Gbit/s data stream. Second, we address superharmonic timing extraction where 40-Gbit/s data lock the fourth harmonic of the 10-GHz oscillator. In the superharmonic timing extraction case, a clock is extracted at 40 GHz as well as its subharmonics at 10, 20, and 30 GHz. [ABSTRACT FROM PUBLISHER]

Experimental and theoretical switching windows in an interferometric configuration with a gain-transparent semiconductor optical amplifier in a loop mirror (GT-SLALOM) are investigated. The amplifier gain and phase dynamics are analyzed in detail. For the gain dynamics, experimental and theoretical pump-probe results are presented. The phase dynamics is investigated theoretically. It is shown that the insertion of an optimized nonreciprocal phase shift in the GT-SLALOM configuration increases the contrast of the switching windows and, thus, improves the performance of the switch for demultiplexing applications. The influence of an asymmetric coupling ratio of the 3-dB input/output coupler on the switching contrast is also discussed [ABSTRACT FROM PUBLISHER]

We investigate the response of a Josephson-coupled multilayer to an ultra-short voltage pulse. The response is understood in terms of the dynamics of the phase differences across the layers, calculated from both the microscopic theory and the resistively shunted junction (RSJ) model. We discuss how such response might play a role in novel multilayered switching devices for use in electronics applications, such as flux quantum digital circuitry. [ABSTRACT FROM PUBLISHER]

A model is used to analyze the gain and phase dynamics of a semiconductor optical amplifier with a carrier reservoir (CR-SOA). Coupled rate equations are solved numerically. Due to the fast transition of carriers from the carrier reservoir layer to the active region, the CR-SOA is shown to have faster gain and phase response than a regular SOA. Increasing the injection current will also decrease the response times. [ABSTRACT FROM PUBLISHER]

This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions. [ABSTRACT FROM AUTHOR]