Frequency and phase synchronization in large groups: Low dimensional description of synchronized clapping, firefly flashing, and cricket chirping

Coordinated rhythms in animal species, including humans: Entrainment from bushcricket chorusing to the philharmonic orchestra

Coordinated group displays featuring precise entrainment of rhythmic behavior between neighbors occur not only in human music, dance and drill, but in the acoustic or optical signaling of a number of species of arthropods and anurans. In this review we describe the mechanisms of phase resetting and phase and tempo adjustments that allow the periodic output of signaling individuals to be aligned in synchronized rhythmic group displays. These mechanisms are well described in some of the synchronizing arthropod species, in which conspecific signals reset an individual's endogenous output oscillators in such a way that the joint rhythmic signals are locked in phase. Some of these species are capable of mutually adjusting both the phase and tempo of their rhythmic signaling, thereby achieving what is called perfect synchrony, a capacity which otherwise is found only in humans. We discuss this disjoint phylogenetic distribution of inter-individual rhythmic entrainment in the context of the functions such entrainment might perform in the various species concerned, and the adaptive circumstances in which it might evolve.

A modification to the Kuramoto model to simulate epileptic seizures as synchronization

The Kuramoto model was developed to describe the coupling of oscillators, motivated by the natural synchronization phenomena. We are interested in modeling an epileptic seizure considering it as the synchronization of action potentials using and modifying this model. In this article, we propose to modify this model, changing the constant coupling force for a function with logistic growth to simulate the onset and epileptic seizure level in an adult male rat caused by the administration of lithium-pilocarpine. Later, we select some frequencies and their respective amplitude values using an algorithm based on the fast Fourier transform (FFT) from an electroencephalography signal when the rat is in basal conditions. Then, we take these values as the natural frequencies of the oscillators in the modified Kuramoto model, considering every oscillator as a single neuron to simulate the emergence of an epileptic seizure numerically by increasing the synchronization value in the coupling function. Finally, using Dynamic Time Warping algorithm, we compare the simulated signal by the Kuramoto model with an FFT approximation of the epileptic seizure.

Population effects driving active material degradation in intercalation electrodes

In battery modeling, the electrode is discretized at the macroscopic scale with a single representative particle in each volume. This lacks the accurate physics to describe interparticle interactions in electrodes. To remedy this, we formulate a model that describes the evolution of degradation of a population of battery active material particles using ideas in population genetics of fitness evolution, where the state of a system depends on the health of each particle that contributes to the system. With the fitness formulation, the model incorporates effects of particle size and heterogeneous degradation effects which accumulate in the particles as the battery is cycled, accounting for different active material degradation mechanisms. At the particle scale, degradation progresses nonuniformly across the population of active particles, observed from the autocatalytic relationship between fitness and degradation. Electrode-level degradation is formed from various contributions of the particle-level degradation, especially from smaller particles. It is shown that specific mechanisms of particle-level degradation can be associated with characteristic signatures in the capacity-loss and voltage profiles. Conversely, certain features in the electrode-level phenomena can also provide insight into the relative importance of different particle-level degradation mechanisms.

Evolutionary Kuramoto dynamics

Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within cells to a complex interconnected unit across an entire organism. The suprachiasmatic nucleus, comprising interconnected oscillatory neurons, serves as a master-clock in mammals. The ubiquity of such systems indicates an evolutionary benefit that outweighs the cost of establishing and maintaining them, but little is known about the process of evolutionary development. To begin to address this shortfall, we introduce and analyse a new evolutionary game theoretic framework modelling the behaviour and evolution of systems of coupled oscillators. Each oscillator is characterized by a pair of dynamic behavioural dimensions, a phase and a communication strategy, along which evolution occurs. We measure success of mutations by comparing the benefit of synchronization balanced against the cost of connections between the oscillators. Despite the simple set-up, this model exhibits non-trivial behaviours mimicking several different classical games—the Prisoner’s Dilemma, snowdrift games, coordination games—as the landscape of the oscillators changes over time. Across many situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization.

Neural Synchrony and Network Dynamics in Social Interaction: A Hyper-Brain Cell Assembly Hypothesis

Mounting neurophysiological evidence suggests that interpersonal interaction relies on continual communication between cell assemblies within interacting brains and continual adjustments of these neuronal dynamic states between the brains. In this Hypothesis and Theory article, a Hyper-Brain Cell Assembly Hypothesis is suggested on the basis of a conceptual review of neural synchrony and network dynamics and their roles in emerging cell assemblies within the interacting brains. The proposed hypothesis states that such cell assemblies can emerge not only within, but also between the interacting brains. More precisely, the hyper-brain cell assembly encompasses and integrates oscillatory activity within and between brains, and represents a common hyper-brain unit, which has a certain relation to social behavior and interaction. Hyper-brain modules or communities, comprising nodes across two or several brains, are considered as one of the possible representations of the hypothesized hyper-brain cell assemblies, which can also have a multidimensional or multilayer structure. It is concluded that the neuronal dynamics during interpersonal interaction is brain-wide, i.e., it is based on common neuronal activity of several brains or, more generally, of the coupled physiological systems including brains.

A physics perspective on collective animal behavior

The beautiful dynamic patterns and coordinated motion displayed by groups of social animals are a beautiful example of self-organization in natural farfrom-equilibrium systems. Recent advances in active-matter physics have enticed physicists to begin to consider how their results can be extended from microscale physical or biological systems to groups of real, macroscopic animals. At the same time, advances in measurement technology have led to the increasing availability of high-quality empirical data for the behavior of animal groups both in the laboratory and in the wild. In this review, I survey this available data and the ways that it has been analyzed. I then describe how physicists have approached synthesizing, modeling, and interpreting this information, both at the level of individual animals and at the group scale. In particular, I focus on the kinds of analogies that physicists have made between animal groups and more traditional areas of physics.

Synchronization of coupled Kuramoto oscillators under resource constraints

A fundamental understanding of synchronized behavior in multiagent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under nonnegligible resource constraints. Here we construct a system of coupled Kuramoto oscillators that consume or produce resources as a function of their oscillation frequency. At high coupling, we observe strongly synchronized dynamics, whereas at low coupling, we observe independent oscillator dynamics as expected from standard Kuramoto models. For intermediate coupling, which typically induces a partially synchronized state, we empirically observe that (and theoretically explain why) the system can exist in either: (i) a state in which the order parameter oscillates in time, or (ii) a state in which multiple synchronization states are simultaneously stable. Whether (i) or (ii) occurs depends upon whether the oscillators consume or produce resources, respectively. Relevant for systems as varied as coupled neurons and social groups, our paper lays important groundwork for future efforts to develop quantitative predictions of synchronized dynamics for systems embedded in environments marked by sparse resources.

Bridging the gap between emotion and joint action

Our daily human life is filled with a myriad of joint action moments, be it children playing, adults working together (i.e., team sports), or strangers navigating through a crowd. Joint action brings individuals (and embodiment of their emotions) together, in space and in time. Yet little is known about how individual emotions propagate through embodied presence in a group, and how joint action changes individual emotion. In fact, the multi-agent component is largely missing from neuroscience-based approaches to emotion, and reversely joint action research has not found a way yet to include emotion as one of the key parameters to model socio-motor interaction. In this review, we first identify the gap and then stockpile evidence showing strong entanglement between emotion and acting together from various branches of sciences. We propose an integrative approach to bridge the gap, highlight five research avenues to do so in behavioral neuroscience and digital sciences, and address some of the key challenges in the area faced by modern societies.

Interactive brains, social minds: Neural and physiological mechanisms of interpersonal action coordination

It is now widely accepted that inter-brain synchronization is an important and inevitable mechanism of interpersonal action coordination and social interaction behavior. This review of the current literature focuses first on the forward model for interpersonal action coordination and functional system theory for biological systems, two broadly similar concepts for adaptive system behavior. Further, we review interacting-brain and/or hyper-brain dynamics studies, to show the interplay between intra- and inter-brain connectivity resulting in hyper-brain network structure and network topology dynamics, and consider the functioning of interacting brains as a superordinate system. The concept of a superordinate system, or superorganism, is then evaluated with respect to neuronal and physiological systems group dynamics, which show further accompanying mechanisms of interpersonal interaction. We note that fundamental problems need to be resolved to better understand the neural mechanisms of interpersonal action coordination.

Dynamic acoustic salience evokes motor responses

Audio-motor integration is currently viewed as a predictive process in which the brain simulates upcoming sounds based on voluntary actions. This perspective does not consider how our auditory environment may trigger involuntary action in the absence of prediction. We address this issue by examining the relationship between acoustic salience and involuntary motor responses. We investigate how acoustic features in music contribute to the perception of salience, and whether those features trigger involuntary peripheral motor responses. Participants with little-to-no musical training listened to musical excerpts once while remaining still during the recording of their muscle activity with surface electromyography (sEMG), and again while they continuously rated perceived salience within the music using a slider. We show cross-correlations between 1) salience ratings and acoustic features, 2) acoustic features and spontaneous muscle activity, and 3) salience ratings and spontaneous muscle activity. Amplitude, intensity, and spectral centroid were perceived as the most salient features in music, and fluctuations in these features evoked involuntary peripheral muscle responses. Our results suggest an involuntary mechanism for audio-motor integration, which may rely on brainstem-spinal or brainstem-cerebellar-spinal pathways. Based on these results, we argue that a new framework is needed to explain the full range of human sensorimotor capabilities. This goal can be achieved by considering how predictive and reactive audio-motor integration mechanisms could operate independently or interactively to optimize human behavior.

Synchronization of complex human networks

The synchronization of human networks is essential for our civilization and understanding its dynamics is important to many aspects of our lives. Human ensembles were investigated, but in noisy environments and with limited control over the network parameters which govern the network dynamics. Specifically, research has focused predominantly on all-to-all coupling, whereas current social networks and human interactions are often based on complex coupling configurations. Here, we study the synchronization between violin players in complex networks with full and accurate control over the network connectivity, coupling strength, and delay. We show that the players can tune their playing period and delete connections by ignoring frustrating signals, to find a stable solution. These additional degrees of freedom enable new strategies and yield better solutions than are possible within current models such as the Kuramoto model. Our results may influence numerous fields, including traffic management, epidemic control, and stock market dynamics.

Null model exhibiting synchronized dynamics in uncoupled oscillators

The phenomenon of phase synchronization of oscillatory systems, arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by nonsynchronous dynamics. How does one guarantee that the observed transient epochs of synchronization are arising from an underlying feedback mechanism and not from some peculiar statistical properties of the system? This question is particularly important for complex biological systems, where the search for a nonexistent feedback mechanism may turn out to be an enormous waste of resources. In this article, we propose a null model for synchronization, motivated by expectations on the dynamical behavior of biological systems, to provide a quantitative measure of the confidence with which one can infer the existence of a feedback mechanism based on observation of transient synchronized behavior. We demonstrate the application of our null model to the phenomenon of gait synchronization in free-swimming nematodes, Caenorhabditis elegans.

Synchronization scenarios in the Winfree model of coupled oscillators

Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.