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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]

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]