Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach

Neural oscillations suggest periodicity encoding during auditory beat processing in the premature brain

When exposed to rhythmic patterns with temporal regularity, adults exhibit an inherent ability to extract and anticipate an underlying sequence of regularly spaced beats, which is internally constructed, as beats are experienced even when no events occur at beat positions (e.g., in the case of rests). Perception of rhythm and synchronization to periodicity is indispensable for development of cognitive functions, social interaction, and adaptive behavior. We evaluated neural oscillatory activity in premature newborns (n = 19, mean age, 32 ± 2.59 weeks gestational age) during exposure to an auditory rhythmic sequence, aiming to identify early traces of periodicity encoding and rhythm processing through entrainment of neural oscillations at this stage of neurodevelopment. The rhythmic sequence elicited a systematic modulation of alpha power, synchronized to expected beat locations coinciding with both tones and rests, and independent of whether the beat was preceded by tone or rest. In addition, the periodic alpha-band fluctuations reached maximal power slightly before the corresponding beat onset times. Together, our results show neural encoding of periodicity in the premature brain involving neural oscillations in the alpha range that are much faster than the beat tempo, through alignment of alpha power to the beat tempo, consistent with observations in adults on predictive processing of temporal regularities in auditory rhythms. RESEARCH HIGHLIGHTS: In response to the presented rhythmic pattern, systematic modulations of alpha power showed that the premature brain extracted the temporal regularity of the underlying beat. In contrast to evoked potentials, which are greatly reduced when there is no sounds event, the modulation of alpha power occurred for beats coinciding with both tones and rests in a predictive way. The findings provide the first evidence for the neural coding of periodicity in auditory rhythm perception before the age of term.

Impact of sensory modality and tempo in motor timing

Background

Accurate motor timing requires the coordinated control of actions in response to external stimuli. Over the past few years, several studies have investigated the effect of sensory input on motor timing; however, the evidence remains conflicting. The purpose of this study was to examine the impact of sensory modality and tempo on the accuracy of timed movements and explore strategies for enhancing motor timing.

Methods

Participants (n = 30) performed synchronization and adaptation circle drawing tasks in virtual reality. In Experiment 1, participants synchronized circle drawing with repeated stimuli based on sensory modalities (auditory, visual, tactile, audio-visual, audio-tactile, and visual-tactile) and tempos (20, 30, and 60 bpm). In Experiment 2, we examined timing adaptation in circle drawing tasks under conditions of unexpected tempo changes, whether increased or decreased.

Results

A significant interaction effect between modality and tempo was observed in the comparison of timing accuracy. Tactile stimuli exhibited significantly higher timing accuracy at 60 bpm, whereas auditory stimuli demonstrated a peak accuracy at 30 bpm. The analysis revealed a significantly larger timing error when adapting to changes in the tempo-down condition compared with the tempo-up condition.

Discussion

Through Experiment 1, we found that sensory modality impacts motor timing differently depending on the tempo, with tactile modality being effective at a faster tempo and auditory modality being beneficial at a moderate tempo. Additionally, Experiment 2 revealed that adapting to changes by correcting timing errors is more challenging with decreasing tempo than with increasing tempo. Our findings suggest that motor timing is intricately influenced by sensory modality and tempo variation. Therefore, to enhance the motor timing, a comprehensive understanding of these factors and their applications is imperative.

A framework for joint music making: Behavioral findings, neural processes, and computational models

Across different epochs and societies, humans occasionally gather to jointly make music. This universal form of collective behavior is as fascinating as it is fragmentedly understood. As the interest in joint music making (JMM) rapidly grows, we review the state-of-the-art of this emerging science, blending behavioral, neural, and computational contributions. We present a conceptual framework synthesizing research on JMM within four components. The framework is centered upon interpersonal coordination, a crucial requirement for JMM. The other components imply the influence of individuals' (past) experience, (current) social factors, and (future) goals on real-time coordination. Our aim is to promote the development of JMM research by organizing existing work, inspiring new questions, and fostering accessibility for researchers belonging to other research communities.

Effects of individual practice on joint musical synchronization

Successful music-making requires precise sensorimotor synchronization, both in individual (solo) and joint (ensemble) social settings. We investigated how individual practice synchronizing with a temporally regular melody (Solo conditions) influences subsequent synchronization between two partners (Joint conditions). Musically trained adults practiced producing a melody by tapping on a keypad; each tap generated the next tone in the melody. First, the pairs synchronized their melody productions with their partner in a baseline Joint synchronization task. Then each partner separately synchronized their melody with a computer-generated recording of the partner's melody in a Solo intervention condition that presented either Normal (temporally regular) auditory feedback or delayed feedback (by 30-70 ms) in occasional (25%) randomly placed tone positions. Then the pairs synchronized again with their partner in a Joint condition. Next, they performed the second Solo condition (normal or delayed auditory feedback) followed again by the Joint condition. Joint synchronization performance was modeled with a delay-coupled oscillator model to assess the coupling strength between partners. Absolute asynchronies in the Solo Intervention tasks were greater in the Delayed feedback condition than in the Normal feedback condition. Model estimates yielded larger coupling values between partners in Joint conditions that followed the Solo Normal feedback than the Solo Delayed feedback. Notably, the asynchronies were smaller in the Joint conditions than in the Solo conditions. These findings indicate that coupled interactions in settings of two or more performers can be improved by individual synchronization practice.

Oscillatory attention in groove

Attention is not constant but rather fluctuates over time and these attentional fluctuations may prioritize the processing of certain events over others. In music listening, the pleasurable urge to move to music (termed 'groove' by music psychologists) offers a particularly convenient case study of oscillatory attention because it engenders synchronous and oscillatory movements which also vary predictably with stimulus complexity. In this study, we simultaneously recorded pupillometry and scalp electroencephalography (EEG) from participants while they listened to drumbeats of varying complexity that they rated in terms of groove afterwards. Using the intertrial phase coherence of the beat frequency, we found that while subjects were listening, their pupil activity became entrained to the beat of the drumbeats and this entrained attention persisted in the EEG even as subjects imagined the drumbeats continuing through subsequent silent periods. This entrainment in both the pupillometry and EEG worsened with increasing rhythmic complexity, indicating poorer sensory precision as the beat became more obscured. Additionally, sustained pupil dilations revealed the expected, inverted U-shaped relationship between rhythmic complexity and groove ratings. Taken together, this work bridges oscillatory attention to rhythmic complexity in relation to musical groove.

Duet synchronization interventions affect social interactions

Humans' complex behavior, such as speech, music, or dance, requires us to coordinate our actions with external sounds as well as with social partners. The presence of a partner can influence individuals' synchronization, and, in turn, social connection with the partner may depend on the degree of synchronization. We manipulated the synchronization quality in intervention conditions to address the causal relationship between observed temporal synchrony and perceived social interaction. Pairs of musician and nonmusician participants first performed a turn-taking task consisting of alternating which partner tapped their melody in synchrony with a metronome (each tap generated the next tone in the melody). In two intervention conditions, participants attempted to synchronize their melodies simultaneously with their partner, either with normal auditory feedback (normal feedback) or randomly placed delayed feedback on 25% of melodic tones (delayed feedback). After each intervention, the turn-taking condition was repeated, and participants completed a questionnaire about connectedness, relationship, and feeling of synchronization with their partner. Results showed that partners' mean asynchronies were more negative following the delayed feedback intervention. In addition, nonmusician partners' tapping variability was larger following the delayed feedback intervention when they had the delayed feedback intervention first. Ratings of connectedness, relationship, and feeling of synchronization with their partner were reduced for all participants after the delayed feedback Intervention. We modeled participants' synchronization performance in the post-intervention turn-taking conditions using delay-coupling oscillator models. Reductions in synchronization performance after delayed feedback intervention were reflected in reduced coupling strength. These findings suggest that turn-taking synchronization performance and social connectedness are altered following short interventions that disrupt synchronization with a partner.

Exploring the dynamics of intentional sensorimotor desynchronization using phasing performance in music

Humans tend to synchronize spontaneously to rhythmic stimuli or with other humans, but they can also desynchronize intentionally in certain situations. In this study, we investigate the dynamics of intentional sensorimotor desynchronization using phasing performance in music as an experimental paradigm. Phasing is a compositional technique in modern music that requires musicians to desynchronize from each other in a controlled manner. A previous case study found systematic nonlinear trajectories in the phasing performance between two expert musicians, which were explained by coordination dynamics arising from the interaction between the intrinsic tendency of synchronization and the intention of desynchronization. A recent exploratory study further examined the dynamics of phasing performance using a simplified task of phasing against a metronome. Here we present a further analysis and modeling of the data from the exploratory study, focusing on the various types of phasing behavior found in non-expert participants. Participants were instructed to perform one phasing lap, and individual trials were classified as successful (1 lap), unsuccessful (> 1 laps), or incomplete (0 lap) based on the number of laps made. It was found that successful phasing required a gradual increment of relative phase and that different types of failure (unsuccessful vs. incomplete) were prevalent at slow vs. fast metronome tempi. The results are explained from a dynamical systems perspective, and a dynamical model of phasing performance is proposed which captures the interaction of intrinsic dynamics and intentional control in an adaptive-frequency oscillator coupled to a periodic external stimulus. It is shown that the model can replicate the multiple types of phasing behavior as well as the effect of tempo observed in the human experiment. This study provides further evidence that phasing performance is governed by the nonlinear dynamics of rhythmic coordination. It also demonstrates that the musical technique of phasing provides a unique experimental paradigm for investigating human rhythmic behavior.

Individual differences of limitation to extract beat from Kuramoto coupled oscillators: Transition from beat-based tapping to frequent tapping with weaker coupling

Musical performers synchronize to each other despite differences in sound-onset timings which reflect each musician's sense of the beat. A dynamical system of Kuramoto oscillators can simulate this spread of onsets at varying levels of temporal alignment with a variety of tempo and sound densities which also influence individual abilities for beat extraction. Here, we examined how people's sense of beat emerges when tapping with Kuramoto oscillators of varying coupling strengths which distribute onsets around periodic moments in time. We hypothesized that people tap regularly close to the sound onset density peaks when coupling is strong. When weaker coupling produces multiple inter-onset intervals that are more widely spread, people may interpret their variety and distributions differently in order to form a sense of beat. Experiment 1 with a small in-person cohort indeed showed a few individuals who responded with high frequency tapping to slightly weak coupled stimuli although the rest found regular beats. Experiment 2 with a larger on-line cohort revealed three groups based on characteristics of inter-tap-intervals analyzed by k-means clustering, namely a Regular group (about 1/3 of the final sample) with the most robust beat extraction, Fast group (1/6) who maintained frequent tapping except for the strongest coupling, and Hybrid group (1/2) who maintained beats except for the weakest coupling. Furthermore, the adaptation time course of tap interval variability was slowest in Regular group. We suggest that people's internal criterion for forming beats may involve different perceptual timescales where multiple stimulus intervals could be integrated or processed sequentially as is, and that the highly frequent tapping may reflect their approach in actively seeking synchronization. Our study provides the first documentation of the novel limits of sensorimotor synchronization and individual differences using coupled oscillator dynamics as a generative model of collective behavior.

Hebbian learning with elasticity explains how the spontaneous motor tempo affects music performance synchronization

A musician's spontaneous rate of movement, called spontaneous motor tempo (SMT), can be measured while spontaneously playing a simple melody. Data shows that the SMT influences the musician's tempo and synchronization. In this study we present a model that captures these phenomena. We review the results from three previously-published studies: solo musical performance with a pacing metronome tempo that is different from the SMT, solo musical performance without a metronome at a tempo that is faster or slower than the SMT, and duet musical performance between musicians with matching or mismatching SMTs. These studies showed, respectively, that the asynchrony between the pacing metronome and the musician's tempo grew as a function of the difference between the metronome tempo and the musician's SMT, musicians drifted away from the initial tempo toward the SMT, and the absolute asynchronies were smaller if musicians had matching SMTs. We hypothesize that the SMT constantly acts as a pulling force affecting musical actions at a tempo different from a musician's SMT. To test our hypothesis, we developed a model consisting of a non-linear oscillator with Hebbian tempo learning and a pulling force to the model's spontaneous frequency. While the model's spontaneous frequency emulates the SMT, elastic Hebbian learning allows for frequency learning to match a stimulus' frequency. To test our hypothesis, we first fit model parameters to match the data in the first of the three studies and asked whether this same model would explain the data the remaining two studies without further tuning. Results showed that the model's dynamics allowed it to explain all three experiments with the same set of parameters. Our theory offers a dynamical-systems explanation of how an individual's SMT affects synchronization in realistic music performance settings, and the model also enables predictions about performance settings not yet tested.

Dynamic models for musical rhythm perception and coordination

Rhythmicity permeates large parts of human experience. Humans generate various motor and brain rhythms spanning a range of frequencies. We also experience and synchronize to externally imposed rhythmicity, for example from music and song or from the 24-h light-dark cycles of the sun. In the context of music, humans have the ability to perceive, generate, and anticipate rhythmic structures, for example, "the beat." Experimental and behavioral studies offer clues about the biophysical and neural mechanisms that underlie our rhythmic abilities, and about different brain areas that are involved but many open questions remain. In this paper, we review several theoretical and computational approaches, each centered at different levels of description, that address specific aspects of musical rhythmic generation, perception, attention, perception-action coordination, and learning. We survey methods and results from applications of dynamical systems theory, neuro-mechanistic modeling, and Bayesian inference. Some frameworks rely on synchronization of intrinsic brain rhythms that span the relevant frequency range; some formulations involve real-time adaptation schemes for error-correction to align the phase and frequency of a dedicated circuit; others involve learning and dynamically adjusting expectations to make rhythm tracking predictions. Each of the approaches, while initially designed to answer specific questions, offers the possibility of being integrated into a larger framework that provides insights into our ability to perceive and generate rhythmic patterns.

How the conception of control influences our understanding of actions

Wilful movement requires neural control. Commonly, neural computations are thought to generate motor commands that bring the musculoskeletal system - that is, the plant - from its current physical state into a desired physical state. The current state can be estimated from past motor commands and from sensory information. Modelling movement on the basis of this concept of plant control strives to explain behaviour by identifying the computational principles for control signals that can reproduce the observed features of movements. From an alternative perspective, movements emerge in a dynamically coupled agent-environment system from the pursuit of subjective perceptual goals. Modelling movement on the basis of this concept of perceptual control aims to identify the controlled percepts and their coupling rules that can give rise to the observed characteristics of behaviour. In this Perspective, we discuss a broad spectrum of approaches to modelling human motor control and their notions of control signals, internal models, handling of sensory feedback delays and learning. We focus on the influence that the plant control and the perceptual control perspective may have on decisions when modelling empirical data, which may in turn shape our understanding of actions.

Brain networks for temporal adaptation, anticipation, and sensory-motor integration in rhythmic human behavior

Human interaction often requires the precise yet flexible interpersonal coordination of rhythmic behavior, as in group music making. The present fMRI study investigates the functional brain networks that may facilitate such behavior by enabling temporal adaptation (error correction), prediction, and the monitoring and integration of information about 'self' and the external environment. Participants were required to synchronize finger taps with computer-controlled auditory sequences that were presented either at a globally steady tempo with local adaptations to the participants' tap timing (Virtual Partner task) or with gradual tempo accelerations and decelerations but without adaptation (Tempo Change task). Connectome-based predictive modelling was used to examine patterns of brain functional connectivity related to individual differences in behavioral performance and parameter estimates from the adaptation and anticipation model (ADAM) of sensorimotor synchronization for these two tasks under conditions of varying cognitive load. Results revealed distinct but overlapping brain networks associated with ADAM-derived estimates of temporal adaptation, anticipation, and the integration of self-controlled and externally controlled processes across task conditions. The partial overlap between ADAM networks suggests common hub regions that modulate functional connectivity within and between the brain's resting-state networks and additional sensory-motor regions and subcortical structures in a manner reflecting coordination skill. Such network reconfiguration might facilitate sensorimotor synchronization by enabling shifts in focus on internal and external information, and, in social contexts requiring interpersonal coordination, variations in the degree of simultaneous integration and segregation of these information sources in internal models that support self, other, and joint action planning and prediction.

Social Interaction and Rate Effects in Models of Musical Synchronization

Important individual differences are observed in people's abilities to synchronize their body movements with regular auditory rhythms. We investigate whether synchronizing with a regular auditory cue is affected by each person's spontaneous production rate (SPR) and by hearing a partner's synchronization in a social context. Musically trained and untrained participants synchronized their tapping with an auditory cue presented at different rates (their own SPR or their partner's SPR) and in a Solo or Joint (turn-taking) condition. Linear and nonlinear oscillator models were fit to participants' mean asynchronies (signed timing differences between the cued onsets and taps). In Joint turn-taking, participants' synchrony was increased when the auditory signal was cued at the participant's own SPR, compared with their partner's SPR; in contrast, synchronization did not differ across rates in the Solo condition. Asynchronies in the Joint task became larger as the difference between partners' spontaneous rates increased; the increased asynchronies were driven by the faster partner who did not slow down to match the rate of their slower partner. Nonlinear delay-coupled models (with time delay, coupling strength, and intrinsic frequency) outperformed linear models (intrinsic frequency only) in accounting for tappers' synchronization adjustments. The nonlinear model's coupling value increased for musically trained participants, relative to untrained participants. Overall, these findings suggest that both intrinsic differences in partners' spontaneous rates and the social turn-taking context contribute to the range of synchrony in the general population. Delay-coupled models are capable of capturing the wide range of individual differences in auditory-motor synchronization.

Mutual beta power modulation in dyadic entrainment

Across a broad spectrum of interactions, humans exhibit a prominent tendency to synchronize their movements with one another. Traditionally, this phenomenon has been explained from the perspectives of predictive coding or dynamical systems theory. While these theories diverge with respect to whether individuals hold internal models of each other, they both assume a predictive or anticipatory mechanism enabling rhythmic interactions. However, the neural bases underpinning interpersonal synchronization are still a subject under active investigation. Here we provide evidence that the brain relies on a common oscillatory mechanism to pace self-generated rhythmic movements and to track the movements produced by a partner. By performing dual-electroencephalography recordings during a joint finger-tapping task, we identified an oscillatory component in the beta range (∼ 20 Hz), which was significantly modulated by both self-generated and other-generated movement. In conditions where the partners perceived each other, we observed periodic fluctuations of beta power as a function of the reciprocal movement cycles. Crucially, this modulation occurred both in visually and in auditorily coupled conditions, and was accompanied by recurrent periods of dyadic synchronized behavior. Our results show that periodic beta power modulations may be a critical mechanism underlying interpersonal synchronization, possibly enabling mutual predictions between coupled individuals, leading to co-regulation of timing and overt mutual adaptation. Our findings thus provide a potential bridge between influential theories attempting to explain interpersonal coordination, and a concrete connection to its neurophysiological bases.

Are We in Time? How Predictive Coding and Dynamical Systems Explain Musical Synchrony

Humans tend to anticipate events when they synchronize their actions with sound (such as when they clap to music), which has puzzled scientists for decades. What accounts for this anticipation? We review two theoretical mechanisms for synchrony: predictive coding and dynamical systems. Both theories are grounded in neural activation patterns, but there are important distinctions. We contrast their assumptions, their computations, and their musical applications to anticipatory synchronization.

Temporal Coordination in Piano Duet Networked Music Performance (NMP): Interactions Between Acoustic Transmission Latency and Musical Role Asymmetries

Today’s audio, visual, and internet technologies allow people to interact despite physical distances, for casual conversation, group workouts, or musical performance. Musical ensemble performance is unique because interaction integrity critically depends on the timing between each performer’s actions and when their acoustic outcomes arrive. Acoustic transmission latency (ATL) between players is substantially longer for networked music performance (NMP) compared to traditional in-person spaces where musicians can easily adapt. Previous work has shown that longer ATLs slow the average tempo in ensemble performance, and that asymmetric co-actor roles and empathy-related traits affect coordination patterns in joint action. Thus, we are interested in how musicians collectively adapt to a given latency and how such adaptation patterns vary with their task-related and person-related asymmetries. Here, we examined how two pianists performed duets while hearing each other’s auditory outcomes with an ATL of 10, 20, or 40 ms. To test the hypotheses regarding task-related asymmetries, we designed duets such that pianists had: (1) a starting or joining role and (2) a similar or dissimilar musical part compared to their co-performer, with respect to pitch range and melodic contour. Results replicated previous clapping-duet findings showing that longer ATLs are associated with greater temporal asynchrony between partners and increased average tempo slowing. While co-performer asynchronies were not affected by performer role or part similarity, at the longer ATLs starting performers displayed slower tempos and smaller tempo variability than joining performers. This asymmetry of stability vs. flexibility between starters and joiners may sustain coordination, consistent with recent joint action findings. Our data also suggest that relative independence in musical parts may mitigate ATL-related challenges. Additionally, there may be a relationship between co-performer differences in empathy-related personality traits such as locus of control and coordination during performance under the influence of ATL. Incorporating the emergent coordinative dynamics between performers could help further innovation of music technologies and composition techniques for NMP.

A metastable attractor model of self-other integration (MEAMSO) in rhythmic synchronization

Human interaction is often accompanied by synchronized bodily rhythms. Such synchronization may emerge spontaneously as when a crowd's applause turns into a steady beat, be encouraged as in nursery rhymes, or be intentional as in the case of playing music together. The latter has been extensively studied using joint finger-tapping paradigms as a simplified version of rhythmic interpersonal synchronization. A key finding is that synchronization in such cases is multifaceted, with synchronized behaviour resting upon different synchronization strategies such as mutual adaptation, leading-following and leading-leading. However, there are multiple open questions regarding the mechanism behind these strategies and how they develop dynamically over time. Here, we propose a metastable attractor model of self-other integration (MEAMSO). This model conceptualizes dyadic rhythmic interpersonal synchronization as a process of integrating and segregating signals of self and other. Perceived sounds are continuously evaluated as either being attributed to self-produced or other-produced actions. The model entails a metastable system with two particular attractor states: one where an individual maintains two separate predictive models for self- and other-produced actions, and the other where these two predictive models integrate into one. The MEAMSO explains the three known synchronization strategies and makes testable predictions about the dynamics of interpersonal synchronization both in behaviour and the brain. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag

Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10 Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.

The influence of performing gesture type on interpersonal musical timing, and the role of visual contact and tempo

Bodily gestures play an important role in the communication of expressive intentions between humans. Music ensemble performance, as an outstanding example of nonverbal human communication, offers an exemplary context to study and understand the gestural control and communication of these expressive intentions. An important mechanism in music ensemble performance is the anticipation and control of interpersonal timing. When performing, musicians are involved in a complex system of mutual adaptation which is not completely understood so far. In this study, we investigated the role of performers' gestures in the mediation process of interpersonal timing in a dyad performance. Therefore, we designed an experiment in which we controlled for the use of hand and arm movements in a musical task, in which dyads were asked to synchronously tap out a melody. Next to their comfortable/natural way of tapping, we instructed participants to either perform pronounced expressive hand and arm gestures in between successive taps, or to restrict from any overt body movement. In addition, we looked at effects of visual contact (yes/no) and tempo (slow: 50 beats per minute; fast: 100 beats per minute). The results show that performers' gestures improve interpersonal musical timing, in terms of the consistency and accuracy of onset asynchronies, and of the variability of produced inter-onset intervals. Interestingly, we found that the use of expressive gestures, in regard to comfortable/natural movements, add to these positive timing effects, but only when there is visual contact and at the slow tempo. In addition, we found that the type of gestures employed by musicians may modulate leader-follower dynamics. Together, these findings are explained by human anticipation mechanisms facilitated by gesturing, shedding new light on the principles underlying human communication of expressive intentions, through music.

Phase bistability between anticipated and delayed synchronization in neuronal populations

Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag, if the receiver also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (with positive phase lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase locking to a bistable regime and eventually to a phase drift. We suggest that our spiking neuronal populations model could be potentially useful to study phase bistability in cortical regions related to bistable perception.