Frequency Entrainment Research Articles

Synchronization in multiplex networks of chaotic oscillators with frequency mismatch

We explore numerically inter-layer synchronization of spatiotemporal patterns in a heterogeneous bilayer network of nonlocally coupled Rössler oscillators. Both layers exhibit phase chimera regimes with similar cluster structures, but there is a mean frequency mismatch between the layers. We show that an entrainment of the mean frequency in the interacting layers is observed already for sufficiently weak inter-layer coupling even when the frequency mismatch is large. At the same time, frequency synchronization does not mean structure synchronization. Our numerical study indicates that inter-layer synchronization takes place within noticeably shorter ranges of the frequency mismatch and the inter-layer coupling strength than the frequency synchronization regime. Besides, we show that the weakest chaotic behavior is observed when both frequency and structure synchronizations occur, while the most developed chaotic oscillations are typical when the spatiotemporal structures in the layers are desynchronized.

Oscillatory Entrainment of the Frequency-following Response in Auditory Cortical and Subcortical Structures.

There is much debate about the existence and function of neural oscillatory mechanisms in the auditory system. The frequency-following response (FFR) is an index of neural periodicity encoding that can provide a vehicle to study entrainment in frequency ranges relevant to speech and music processing. Criteria for entrainment include the presence of poststimulus oscillations and phase alignment between stimulus and endogenous activity. To test the hypothesis of entrainment, in experiment 1 we collected FFR data for a repeated syllable using magnetoencephalography (MEG) and electroencephalography in 20 male and female human adults. We observed significant oscillatory activity after stimulus offset in auditory cortex and subcortical auditory nuclei, consistent with entrainment. In these structures, the FFR fundamental frequency converged from a lower value over 100 ms to the stimulus frequency, consistent with phase alignment, and diverged to a lower value after offset, consistent with relaxation to a preferred frequency. In experiment 2, we tested how transitions between stimulus frequencies affected the MEG FFR to a train of tone pairs in 30 people. We found that the FFR was affected by the frequency of the preceding tone for up to 40 ms at subcortical levels, and even longer durations at cortical levels. Our results suggest that oscillatory entrainment may be an integral part of periodic sound representation throughout the auditory neuraxis. The functional role of this mechanism is unknown, but it could serve as a fine-scale temporal predictor for frequency information, enhancing stability and reducing susceptibility to degradation that could be useful in real-life noisy environments.SIGNIFICANCE STATEMENT Neural oscillations are proposed to be a ubiquitous aspect of neural function, but their contribution to auditory encoding is not clear, particularly at higher frequencies associated with pitch encoding. In a magnetoencephalography experiment, we found converging evidence that the frequency-following response has an oscillatory component according to established criteria: poststimulus resonance, progressive entrainment of the neural frequency to the stimulus frequency, and relaxation toward the original state on stimulus offset. In a second experiment, we found that the frequency and amplitude of the frequency-following response to tones are affected by preceding stimuli. These findings support the contribution of intrinsic oscillations to the encoding of sound, and raise new questions about their functional roles, possibly including stabilization and low-level predictive coding.

Speech-Brain Frequency Entrainment of Dyslexia with and without Phonological Deficits.

Developmental dyslexia is a cognitive disorder characterized by difficulties in linguistic processing. Our purpose is to distinguish subtypes of developmental dyslexia by the level of speech–EEG frequency entrainment (δ: 1–4; β: 12.5–22.5; γ1: 25–35; and γ2: 35–80 Hz) in word/pseudoword auditory discrimination. Depending on the type of disabilities, dyslexics can divide into two subtypes—with less pronounced phonological deficits (NoPhoDys—visual dyslexia) and with more pronounced ones (PhoDys—phonological dyslexia). For correctly recognized stimuli, the δ-entrainment is significantly worse in dyslexic children compared to controls at a level of speech prosody and syllabic analysis. Controls and NoPhoDys show a stronger δ-entrainment in the left-hemispheric auditory cortex (AC), anterior temporal lobe (ATL), frontal, and motor cortices than PhoDys. Dyslexic subgroups concerning normolexics have a deficit of δ-entrainment in the left ATL, inferior frontal gyrus (IFG), and the right AC. PhoDys has higher δ-entrainment in the posterior part of adjacent STS regions than NoPhoDys. Insufficient low-frequency β changes over the IFG, the inferior parietal lobe of PhoDys compared to NoPhoDys correspond to their worse phonological short-term memory. Left-dominant 30 Hz-entrainment for normolexics to phonemic frequencies characterizes the right AC, adjacent regions to superior temporal sulcus of dyslexics. The pronounced 40 Hz-entrainment in PhoDys than the other groups suggest a hearing “reassembly” and a poor phonological working memory. Shifting up to higher-frequency γ-entrainment in the AC of NoPhoDys can lead to verbal memory deficits. Different patterns of cortical reorganization based on the left or right hemisphere lead to differential dyslexic profiles.

Locking and regularization of chimeras by periodic forcing

We study how a chimera state in a one-dimensional medium of nonlocally coupled oscillators responds to a homogeneous in space periodic in time external force. On a macroscopic level, where a chimera can be considered as an oscillating object, forcing leads to entrainment of the chimera's basic frequency inside an Arnold tongue. On a mesoscopic level, where a chimera can be viewed as an inhomogeneous, stationary, or nonstationary pattern, strong forcing can lead to regularization of an unstationary chimera. On a microscopic level of the dynamics of individual oscillators, forcing outside of the Arnold tongue leads to a multiplateau state with nontrivial locking properties.

Spiking neural state machine for gait frequency entrainment in a flexible modular robot

We propose a modular architecture for neuromorphic closed-loop control based on bistable relaxation oscillator modules consisting of three spiking neurons each. Like its biological prototypes, this basic component is robust to parameter variation but can be modulated by external inputs. By combining these modules, we can construct a neural state machine capable of generating the cyclic or repetitive behaviors necessary for legged locomotion. A concrete case study for the approach is provided by a modular robot constructed from flexible plastic volumetric pixels, in which we produce a forward crawling gait entrained to the natural frequency of the robot by a minimal system of twelve neurons organized into four modules.

Relaxation oscillations and frequency entrainment in quantum mechanics.

Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary nonlinearities. The previously known steady state of such quantum oscillators in the weakly nonlinear regime (also known as a Stuart-Landau oscillator) is shown to emerge as a special case. Most importantly, the hallmark of strong nonlinearity-relaxation oscillations-is shown in quantum mechanics. Depending on the oscillator's nonlinearity, relaxation oscillations are found to occur via two distinct mechanisms in phase space.

Electrophysiological evidence for action-effect prediction.

A central function of the human brain is prediction. Influential theoretical views suggest that we form predictions about forthcoming sensory outcomes that follow from our own actions and that anticipation of these outcomes is fundamental for action control. However, little is known about how predicted outcomes are represented at the neural level. We hypothesized that neural activity reflecting the anticipation of outcomes should precede action initiation. Following computational theories on action control, anticipation should be reflected in an outcome-selective reduction in neural activity. To test this, the present study recorded scalp electroencephalography to show that brain activity reflects action-effect specific representations before response initiation. We harnessed frequency entrainment to tag neural activity specific for particular action-effects. Participants engendered visual action-effects that were presented in flickering frequencies of 6 or 10 Hz, either according to a fixed cue-response mapping (Experiment 1) or freely chosen (Experiment 2). Results showed that perception of action-effects entrained a steady-state visual brain response specific to the perceived action-effect at either 6 or 10 Hz. More important, neural pattern reflecting action-effect specific representations emerged even before a response was given (i.e., without any visual stimulation). In line with theoretical accounts, perception of action-effects led to a specific increase in neural activity, while prediction of action-effects led to a specific decrease in neural activity. These findings provide neural evidence for the anticipation of action-effects before response initiation, supporting major theories of action control. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

The Relationship between Prosodic Ability and Conversational Prosodic Entrainment.

Conversational entrainment or alignment-the convergence of conversation partners over the course of a conversation in a variety of linguistic features-is a well-attested conversational phenomenon. The research on prosodic entrainment has shown correlations between prosodic entrainment and several social dimensions of rapport between conversation partners. However, little is known about how skill-level in the entrainment domain affects the ability to converge during a conversation. The goal of the current study was to investigate whether skill-level of a speaker in receptive and expressive word, sentence, and emotional prosody is correlated with the amount of prosodic entrainment contributed at the conversational level. Twenty native speakers of American English were paired into ten dyads of seven female/female and three female/male conversation pairs. Conversations for each pair were recorded and analyzed. Test scores measuring word, sentence, and emotional prosody were correlated with the amount of fundamental frequency entrainment during conversations. The results indicate that a negative correlation exists between expressive prosody skill and the amount of f0 entrainment contributed by a speaker. This suggests that speakers with better expressive prosodic skills at the word and sentence level entrain less to their conversation partners. Receptive prosody ability was not correlated with conversational prosodic entrainment.

Sperm chemotaxis is driven by the slope of the chemoattractant concentration field.

Spermatozoa of marine invertebrates are attracted to their conspecific female gamete by diffusive molecules, called chemoattractants, released from the egg investments in a process known as chemotaxis. The information from the egg chemoattractant concentration field is decoded into intracellular Ca2+ concentration ([Ca2+]i) changes that regulate the internal motors that shape the flagellum as it beats. By studying sea urchin species-specific differences in sperm chemoattractant-receptor characteristics we show that receptor density constrains the steepness of the chemoattractant concentration gradient detectable by spermatozoa. Through analyzing different chemoattractant gradient forms, we demonstrate for the first time that Strongylocentrotus purpuratus sperm are chemotactic and this response is consistent with frequency entrainment of two coupled physiological oscillators: i) the stimulus function and ii) the [Ca2+]i changes. We demonstrate that the slope of the chemoattractant gradients provides the coupling force between both oscillators, arising as a fundamental requirement for sperm chemotaxis.

Development of Vibratory Conveyor System Using Frequency Entrainment for Underactuated Walking of Rimless Wheel

In this paper, we propose a novel vibratory conveyor system based on frequency entrainment of limit cycle walking. The conveyor system transports a passive rimless wheel utilizing a vibratory plate which moves up and down by rolling and impact of an active rimless wheel. First, we introduce the mathematical model of the proposed conveyor system. Next, we investigate the influence for the passive rimless wheel gait by vibration of the conveyance plate via the numerical simulation using the mathematical model, and confirm the entrainment phenomenon between the passive rimless wheel and the vibratory plate. Futermore, we conduct experiments using the prototype vibratory conveyor system, and confirm that experimental results show similar trends to the numerical simulation.

Prominent Precession Band Variance in ENSO Intensity Over the Last 300,000 Years

AbstractThree transient National Center for Atmospheric Research Community Climate System Model, version 3 model simulations were analyzed to study the responses of El Niño–Southern Oscillation (ENSO) and the equatorial Pacific annual cycle (AC) to external forcings over the last 300,000 years. The time‐varying boundary conditions of insolation, greenhouse gases, and continental ice sheets, accelerated by a factor of 100, were sequentially added in these simulations. The simulated ENSO and AC amplitudes change in phase, and both have pronounced precession band variance (~21,000 years). The precession‐modulated slow (orbital time scales) ENSO evolution is dominated linearly by the change of the coupled ocean‐atmosphere instability, notably the Ekman upwelling feedback and thermocline feedback. In contrast, the greenhouse gases and ice sheet forcings (~100,000‐year cycles) are opposed to each other as they influence ENSO variability through changes in AC amplitude via a common nonlinear frequency entrainment mechanism. The acceleration technique could dampen and delay the precession signals below the surface ocean associated with ENSO intensity.

Alpha Frequency Entrainment Reduces the Effect of Visual Distractors.

Numerous studies have linked alpha frequency (∼10 Hz) visual entrainment to the inhibition of incoming visual information. However, although these studies have provided key evidence for the intrinsic sensitivity of the human brain to incoming alpha frequency signals, they have only examined the negative impact of alpha entrainment on target stimuli. Thus, it remains uncertain whether the perception of distracting or nonimperative stimuli can also be affected by alpha frequency entrainment. In the current study, we address this question using an adapted version of the arrow-based Erikson "flanker" paradigm that incorporates stimuli flickering at two distinct frequencies: 10 Hz (alpha) and 30 Hz. By presenting flickering stimuli in the portions of the visual field where the flanking arrows would soon appear, we aimed to determine whether the frequency of visual entrainment (i.e., 10 Hz vs. 30 Hz) significantly interacted with the congruency of the flanking arrows (representing selective attention processing) using behavioral task performance and neural oscillations as the outcome metrics. Twenty-three healthy adult participants underwent magnetoencephalography during performance of the task. Our results indicated a reduced congruency effect (i.e., a smaller difference between congruent and incongruent trials) in the alpha flicker condition, as compared with the 30-Hz flicker condition, which suggests a robust relationship between alpha entrainment and the active inhibition of distractor stimuli appearing in that portion of the visual field. Supporting this, alpha frequency (but not 30 Hz) entrainment responses in the primary visual cortex also covaried significantly with the behavioral congruency effect.

Preliminary Neurophysiological Evidence of Altered Cortical Activity and Connectivity With Neurologic Music Therapy in Parkinson's Disease.

Neurologic Music Therapy (NMT) is a novel impairment-focused behavioral intervention system whose techniques are based on the clinical neuroscience of music perception, cognition, and production. Auditory Stimulation (RAS) is one of the NMT techniques, which aims to develop and maintain a physiological rhythmic motor activity through rhythmic auditory cues. In a series of breakthrough studies beginning in the mid-nineties, we discovered that RAS durably improves gait velocity, stride length, and cadence in Parkinson's disease (PD). No study to date reports the neurophysiological evidence of auditory-motor frequency entrainment after a NMT intervention in the Parkinson's community. We hypothesized that NMT-related motor improvements in PD are due to entrainment-related coupling between auditory and motor activity resulting from an increased functional communication between the auditory and the motor cortices. Spectral analysis in the primary motor and auditory cortices during a cued finger tapping task showed a simultaneous increase in evoked power in the beta-range along with an increased functional connectivity after a course of NMT in a small sample of three older adults with PD. This case study provides preliminary evidence that NMT-based motor rehabilitation may enhance cortical activation in the auditory and motor areas in a synergic manner. With a lack of both control subjects and control conditions, this neuroimaging case-proof of concept series of visible changes suggests potential mechanisms and offers further education on the clinical applications of musical interventions for motor impairments.

Rhythmic modulation of thalamic oscillations depends on intrinsic cellular dynamics

Objective. Rhythmic brain stimulation has emerged as a powerful tool to modulate cognition and to target pathological oscillations related to neurological and psychiatric disorders. However, we lack a systematic understanding of how periodic stimulation interacts with endogenous neural activity as a function of the brain state and target. Approach. To address this critical issue, we applied periodic stimulation to a unified biophysical thalamic network model that generates multiple distinct oscillations, and examined thoroughly the impact of rhythmic stimulation on different oscillatory states. Main results. We found that rhythmic perturbation induces four basic response mechanisms: entrainment, acceleration, resonance and suppression. Importantly, the appearance and expression of these mechanisms depend highly on the intrinsic cellular dynamics in each state. Specifically, the low-threshold bursting of thalamocortical cells (TCs) in delta (δ) oscillation renders the network relatively insensitive to entrainment; the high-threshold bursting of TCs in alpha (α) oscillation leads to widespread oscillation suppression while the tonic spiking of TC cells in gamma (γ) oscillation results in prominent entrainment and resonance. In addition, we observed entrainment discontinuity during α oscillation that is mediated by firing pattern switching of high-threshold bursting TC cells. Furthermore, we demonstrate that direct excitatory stimulation of the lateral geniculate nucleus (LGN) entrains thalamic oscillations via an asymmetric Arnold tongue that favors higher frequency entrainment and resonance, while stimulation of the inhibitory circuit, the reticular nucleus, induces much weaker and more symmetric entrainment and resonance. These results support the notion that rhythmic stimulation engages brain oscillations in a state- and target-dependent manner. Significance. Overall, our study provides, for the first time, insights into how the biophysics of thalamic oscillations guide the emergence of complex, state-dependent mechanisms of target engagement, which can be leveraged for the future rational design of novel therapeutic stimulation modalities.

Injection locking of multiple auto-oscillation modes in a tapered nanowire spin Hall oscillator

Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/Ni80Fe20(5 nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self-localized spin-wave bullets that oscillate at two distinct frequencies (5.2 GHz and 5.45 GHz) and are localized at different positions separated by about 750 nm within the SHO. This state of a tapered SHO has been predicted by a Ginzburg-Landau auto-oscillator model, but not yet been directly confirmed experimentally. We demonstrate that the observed bullets can be individually synchronized to external microwave signals, leading to a frequency entrainment, linewidth reduction and increase in oscillation amplitude for the bullet that is selected by the microwave frequency. At the same time, the amplitude of other parasitic modes decreases, which promotes the single-mode operation of the SHO. Finally, the synchronization of the spin-wave bullets is studied as a function of the microwave power. We believe that our findings promote the realization of extended spin Hall oscillators accomodating several distinct spin-wave bullets, that jointly cover an extended range of tunability.

Author Correction: Gamma frequency entrainment attenuates amyloid load and modifies microglia.

Change history: In this Article, Extended Data Fig. 8 and Extended Data Table 1 contained errors, which have been corrected online.

The emergence of multistability and chaos in a two-mode van der Pol generator versus different connection types of linear oscillators

In this work, we study the multistability and chaos phenomena in a classical two-mode van der Pol generator which consists of a nonlinear element and two linear oscillators. We show that the configuration of the connections of the linear oscillators in the two-mode self-oscillating system significantly affects its oscillation regimes and bifurcational transitions. In the case of the feedback loop including one oscillator, the two-mode system demonstrates the well-known effect of frequency entrainment, including bistability and hysteresis phenomena. If the feedback loop involves both linear oscillators, the entrainment effect disappears; however, two new complex regimes of quasi-periodicity and chaotic self-oscillations emerge. We present here the results of the bifurcation analysis of the multistability formation and transition to chaos.

Robust neuronal oscillatory entrainment to speech displays individual variation in lateralisation

ABSTRACTNeural oscillations may be instrumental for the tracking and segmentation of continuous speech. Earlier work has suggested that delta, theta and gamma oscillations entrain to the speech rhythm. We used magnetoencephalography and a large sample of 102 participants to investigate oscillatory entrainment to speech, and observed robust entrainment of delta and theta activity, and weak group-level gamma entrainment. We show that the peak frequency and the hemispheric lateralisation of the entrainment are subject to considerable individual variability. The first finding may support the involvement of intrinsic oscillations in entrainment, and the second finding suggests that there is no systematic default right-hemispheric bias for processing acoustic signals on a slow time scale. Although low frequency entrainment to speech is a robust phenomenon, the characteristics of entrainment vary across individuals, and this variation is important for understanding the underlying neural mechanisms of entrainment, as well as its functional significance.

Individual and dyadic rope turning as a window into social coordination

The spontaneous and intentional movement coordination between peoples is well understood. Less is known about such interactions when the coordination is subordinate to the task and when the task involves, next to vision, mechanically induced haptic and kinesthetic coupling between dyadic partners. We therefore investigated dyadic jump rope turning. Fifteen dyadic pairs conjointly turned a jump rope to which five markers were equidistantly attached, and whose movements were recorded in 3D. In addition, each participant turned one side of the rope while the other side was quasi-fixed in an individual baseline condition. The participants’ goal was to turn the rope regularly and smoothly. Individual spontaneous turning frequencies differed substantially across participants. Yet, dyadic pairs spontaneously turned the rope at a common frequency, indicative of frequency entrainment. The dyadic rope rotations were less variable despite weaker between near-hand marker coordination than the individual rope rotations, and the degree of performance improvement was most pronounced for participants who were paired with a partner who performed better in the individual condition. The direction and relative strength of the coupling between partners varied substantially across dyads, but the degree of coupling asymmetry had no substantial effect on the rope tuning quality. The absolute degree in which dyadic partners adjusted to each other, however, scaled moderately with their turning performance. Although the individual performances did not predict the dyadic performances, the difference in individual performance between dyadic partners had some predictive value for the dyadic performance. In combination, these results indicate that the partners were functionally adapting to each other in order to satisfy the task goal and suggest that the relative performance differences rather than the individual performances has predictive value for conjoint action.

Synchronization in pairs of rotating active biomotors.

Although synchronization is a well-known physical phenomenon, experimental studies of its emergence in living bacterial cells are still scarce. The difficulty in generating a controlled scenario to detect synchronization has limited the experimental outcomes so far. We present a realization based on holographic optical tweezers in which adhered pairs of self-propelled bacteria rotate in a plane. The separation distance between the bacteria determines the strength of the hydrodynamic coupling. Despite the noisy environment and autonomous dynamics of the living bacteria, we find evidence of phase locking and frequency entrainment in their rotation. The observation of higher order frequency synchronization is also discussed.