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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]

Macroscopic oscillations in the brain are involved in various cognitive and physiological processes, yet their precise function is not completely understood. Communication through coherence (CTC) theory proposes that these rhythmic electrical patterns might serve to regulate the information flow between neural populations. Thus, to communicate effectively, neural populations must synchronize their oscillatory activity, ensuring that input volleys from the presynaptic population reach the postsynaptic one at its maximum phase of excitability. We consider an Excitatory–Inhibitory (E–I) network whose macroscopic activity is described by an exact mean-field model. The E–I network receives periodic inputs from either one or two external sources, for which effective communication will not be achieved in the absence of control. We explore strategies based on optimal control theory for phase–amplitude dynamics to design a periodic control that sets the target population in the optimal phase to synchronize its activity with a specific presynaptic input signal and establish communication. The control mechanism resembles the role of a higher cortical area in the context of selective attention. To design the control, we use the phase–amplitude reduction of a limit cycle and leverage recent developments in this field in order to find the most effective control strategy regarding a defined cost function. Furthermore, we present results that guarantee the local controllability of the system close to the limit cycle. • Optimal-control strategies provide controls that suitably adjust the dynamics for enhanced communication. • Controlled synchronization is decisive for effective communication in mean-field models of E–I networks. • Using phase–amplitude description, optimal periodic controls minimally alter the oscillation, while enhance communication. [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.

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.

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]

• Joule heating phenomenon is incorporated in the AC Josephson effect. • The phase and temperature dynamic states are discussed for various parameters. • Device state diagrams are realized for Josephson weak-link – shunted and unshunted. • A useful thermal model as a guide for the experiments with weak-link-based devices. Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics and inevitable Joule heating in a JJ leads to new characteristics. Here, we report a time-dependent model incorporating thermal effect in the AC Josephson regime for a Josephson WL shunted by a resistor together with an inductor to investigate the dynamics as well as the resulting current-voltage characteristics. We find that the dynamic regime where phase and temperature oscillate simply widens due to a pure resistive shunt. However, a significant inductive time-scale in the shunt loop, competing with the thermal time-scale, introduces high-frequency relaxation oscillations in the dynamic regime. Based on numerical analysis, we present state diagrams for different parameter regimes. Our model is a guide for better controlling the parameters in the experiments of WL-based devices. [ABSTRACT FROM AUTHOR]

A novel structural dynamic model for free standing hybrid riser (FSHR) is established based on the absolute nodal coordinate formulation (ANCF) in the present study. The position and slope coordinates are used in global framework to avoid coordinate transformation, and an accurate geometric relationship is introduced to describe geometric nonlinearity. The current loads on the risers and buoyancy can are simulated by Morrison equation and wake oscillator, respectively. After case validations, the vortex-induced motion (VIM) regimes of the buoyancy can and the phase dynamics of the riser and jumper in a FSHR system, subjected to the ocean current and vessel motion, is numerically investigated. It is found that the VIM of the buoyancy can experiences multiple motion switches among the periodic, quasiperiodic, multiple periodic, transition I and transition II regimes under different vessel motions. The y -motion of the jumper and both x - and y -motions of the riser present the phase trapping phenomenon along the structures. The phase trapping and locking, phase drifting and slipping, and other states are observed for x -motion of the jumper, which form a shape of "fish head" with opening mouth towards lower amplitude or higher period of vessel motion in regime map. • A novel structural dynamic model for FSHR system is established based on the ANCF. • Periodic, quasiperiodic, multiple periodic, transition I and II regimes of VIM are found under different vessel motions. • Three transition and multiple periodic bands are interspersed in the quasiperiodic regime of VIM. • The phase trapping and locking, drifting and slipping, and other states are captured for in-line motion along the jumper. • The phase dynamics of the jumper form a shape of "fish head" in the regime map. [ABSTRACT FROM AUTHOR]