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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.

The radiation dynamics of a closed chain of lasers with optoelectronic delayed coupling is analyzed. We consider bidirectional couplings of two designs: (i) diffusion type with feedback and (ii) bidirectional type without feedback. Assuming that the number of lasers is sufficiently large, we propose integro-differential models for spatially distributed variables with periodic boundary conditions. The critical value of the coupling coefficient is determined at which the stationary state of laser generation spontaneously becomes unstable due to the presence of a delay in the coupling lines. Bifurcations of asymptotically infinite dimension are described. For both types of coupling, we obtain the same two-dimensional complex partial differential equation of the Ginzburg–Landau type (with the difference only in the coefficients) for the slowly varying amplitude of the fundamental harmonic. Using the simplest homogeneous solution of such a quasi-normal form, the oscillations of laser radiation in chains, which can be anti-phase or in-phase depending on the time delay and the design of the couplings, are analytically described. • The models of a large laser chain with bidirectional couplings are proposed. • Bifurcations of infinite dimension are studied in dependence on coupling delay. • Boundary-value problems are obtained as quasi-normal forms. • The delay-dependent direction (super- or subcritical) of bifurcation is determined. • Delay intervals leading to anti- or in-phase oscillations in laser chain are obtained. [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]

We study fast and slow clustering dynamics of Cucker–Smale ensemble with internal phase dynamics via the Cucker–Smale–Kuramoto (in short, CSK) model. The CSK model describes the emergent dynamics of flocking particles with phase dynamics. It consists of the Cucker–Smale flocking model and the Kuramoto model, and their interplay is registered in the communication weight function between particles. We present a sufficient framework for mono-cluster flocking and complete synchronization in terms of system parameters and initial data. In particular, the mono-cluster flocking will emerge exponentially fast (fast dynamics). On the other hand, when initial spatial-velocity configuration is close to the bi-cluster flocking, we also provide a sufficient framework leading to convergence of bi-cluster flocking algebraically slow depending on the decay rate of the communication weight (slow flocking dynamics). We also provide several numerical examples and compare them with analytical results. [ABSTRACT FROM AUTHOR]

This study numerically investigates the influence of the taper on the flow-induced vibrations of an elastically mounted circular cylinder under vortex-induced vibrations (VIV). The dynamic response of three different taper ratios [ T R defined as T R = l / (d 2 − d 1) = 12 (highly tapered cylinder), 20 (medium tapered cylinder), and 40 (low tapered cylinder)], where d1 and d2 are the largest and smallest diameter of the tapered cylinder, respectively, with length l is studied at a fixed Reynolds number [ Re D , defined based on the averaged cylinder diameter, D = (d 1 + d 2) / 2 ] of 150. The amplitude and frequency response of the tapered cylinder is characterized by a low mass ratio (defined as the ratio of the total oscillating mass to the displaced fluid mass) of m* = 2 over the wide range of reduced velocity (3 ≤ U r ≤ 16) covering the full amplitude-response spectrum (based on the oscillation amplitude) of the VIV. The results show the existence of difference in the spanwise shedding of vortices owing to the poor spanwise pressure correlation. The flow field analysis in the wake of the oscillating cylinder reveals the dominance of the three-dimensional structures in the wake (near the top end with the larger diameter) behind the cylinder with the increase in the taper ratio (even at such low Re D where the uniform cylinder exhibits the two-dimensional wake). Also, the tapered cylinder exhibits a wide range of frequency synchronization (i.e., wide lock-in area) compared to the uniform cylinder. Tapering the cylinder results in the shift of the peak of the max oscillation amplitude or, in turn, the shift in the transitioning of the response branches. Further, force decomposition, energy transfer, and phase dynamics are also discussed for the taper cylinders. [ABSTRACT FROM AUTHOR]

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractiveâ€"repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static Ď€, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuartâ€"Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling. [ABSTRACT FROM AUTHOR]

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, f1 and f2. On increasing the forcing amplitude, xf, at a fixed forcing frequency, ff, we find two different types of synchronization: (i) ff/f1 = 1: 1 or 2: 1 chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to 1: 1 CDS, the system transitions from an unforced chaotic state (CH1,2) to a forced chaotic state (CH1,2,f), then to a two-frequency quasiperiodic state where chaos is destroyed (T²2,f), and finally to a phase-locked period-1 state (P1f). The route to 2: 1 CDS is similar, but the quasiperiodic state hosts a doubled torus (2T²2,f) that transforms into a phase-locked period-2 orbit (P2f) when CDS occurs. En route to PSC, the system transitions to a forced chaotic state (CH1,2,f) followed by a phase-locked chaotic state, where f1, f2 and ff still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical xf required for the onset of CDS does not vary significantly with ff. We then use two unidirectionally coupled Anishchenko-Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to 1: 1 CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the ff/f1-xf plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control. [ABSTRACT FROM AUTHOR]

We study the collective behaviors of the fractional Kuramoto model (FKM) proposed in [16] with general interaction network topologies and present a new hybrid fractional Kuramoto (HFKM) model for synchronization. Here, our proposed HFKM model consists of continuous evolution processes and a sequence of discrete processes. The continuous dynamics between discrete times is governed by the fractional Kuramoto (FKM) model, whereas a sequence of discrete processes governs the reinitialization of data by deleting past memory of phase dynamics except for the current state and changing interaction network topologies. For the proposed models, we provide sufficient conditions for the emergence of practical synchronization for nonidentical oscillators and phase synchronization for identical oscillators, respectively. This improves the earlier work [16] on the slow relaxation of the FKM model. [ABSTRACT FROM AUTHOR]

Synchronization is common in both nature and human physiology, often used to illustrate nonlinear dynamics. Interestingly, one can initiate their comprehension of this phenomenon from pure linear systems. In this Tutorial, we begin with a theoretical exploration of coupled oscillators' dynamic behavior, enabling us to discern and contrast the unique attributes of dissipative coupling as opposed to commonly observed coherent coupling. We then examine synchronization in two dissipative coupled linear systems: one with two pendulums mutually linked via the Lenz effect and the other with two RLC oscillators coupled via a resistor. This Tutorial is designed to serve as a concise starting point for researchers interested in exploring synchronization phenomena using a simplified model driven solely by dissipative coupling. [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]

We consider the effect of an external periodic force on chimera states in the phase oscillator model proposed in [Phys. Rev. Lett, v. 101, 00319007 (2008)]. Using the Ott – Antonsen reduction, the dynamical equations for the global order parameter characterizing the degree of synchronization are constructed. The frequency locking by an external periodic force region is constructed. The possibility of stable chimeras synchronization and unstable chimeras stabilization is established. The instability development of the chimera states leads to the appearance of breather chimeras or complete synchronization. [ABSTRACT FROM AUTHOR]

Swarmalators are oscillators that swarm through space as they synchronize in time. Introduced a few years ago to model many systems that mix synchrony with self-assembly, they remain poorly understood theoretically. Here, we obtain the first analytic results on swarmalators moving in two spatial dimensions by introducing a simplified model where the swarmalators have no hard-shell interaction terms and move on a periodic plane. These simplifications allow expressions for order parameters, stabilities and bifurcations to be derived exactly. [ABSTRACT FROM AUTHOR]

Background: This study utilized recent advancements in electroencephalography (EEG) technology that enable the measurement of prefrontal event-related potentials (ERPs) to facilitate the early detection of mild cognitive impairment (MCI). We investigated two-channel prefrontal ERP signals obtained from a large cohort of elderly participants and compare among cognitively normal (CN), subjective cognitive decline (SCD), amnestic MCI (aMCI), and nonamnestic MCI (naMCI) groups. Methods: Signal processing and ERP component analyses, specifically adapted for two-channel prefrontal ERP signals evoked by the auditory oddball task, were performed on a total of 1,754 elderly participants. Connectivity analyses were conducted to assess brain synchronization, especially in the beta band involving the phase locking value (PLV) and coherence (COH). Time-frequency, time-trial, grand average, and further statistical analyses of the standard and target epochs were also conducted to explore differences among the cognition groups. Results: The MCI group’s response to target stimuli was characterized by greater response time variability (p < 0.001) and greater variability in the P300 latency (p < 0.05), leading to less consistent responses than those of the healthy control (HC) group (CN+SCD subgroups). In the connectivity analyses of PLV and COH waveforms, significant differences were observed, indicating a loss of synchronization in the beta band in response to standard stimuli in the MCI group. In addition, the absence of event-related desynchronization (ERD) indicated that information processing related to readiness and task performance in the beta band was not efficient in the MCI group. Furthermore, the observed decline in the P200 amplitude as the standard trials progressed suggests the impaired attention and inhibitory processes in the MCI group compared to the HC group. The aMCI subgroup showed high variability in COH values, while the naMCI subgroup showed impairments in their overall behavioral performance. Conclusion: These findings highlight the variability and connectivity measures can be used as markers of early cognitive decline; such measures can be assessed with simple and fast two-channel prefrontal ERP signals evoked by both standard and target stimuli. Our study provides deeper insight of cognitive impairment and the potential use of the prefrontal ERP connectivity measures to assess early cognitive decline. [ABSTRACT FROM AUTHOR]

The brain is a complex non-equilibrium system capable of expressing many different dynamics as well as the transitions between them. We hypothesized that the level of non-equilibrium can serve as a signature of a given brain state, which was quantified using the arrow of time (the level of irreversibility). Using this thermodynamic framework, the irreversibility of emergent cortical activity was quantified from local field potential recordings in male Lister-hooded rats at different anesthesia levels and during the sleep-wake cycle. This measure was carried out on five distinct brain states: slow-wave sleep, awake, deep anesthesia–slow waves, light anesthesia–slow waves, and microarousals. Low levels of irreversibility were associated with synchronous activity found both in deep anesthesia and slow-wave sleep states, suggesting that slow waves were the state closest to the thermodynamic equilibrium (maximum symmetry), thus requiring minimum energy. Higher levels of irreversibility were found when brain dynamics became more asynchronous, for example, in wakefulness. These changes were also reflected in the hierarchy of cortical dynamics across different cortical areas. The neural dynamics associated with different brain states were characterized by different degrees of irreversibility and hierarchy, also acting as markers of brain state transitions. This could open new routes to monitoring, controlling, and even changing brain states in health and disease. [ABSTRACT FROM AUTHOR]

The synchronization phenomenon in nature has been utilized in sensing and timekeeping fields due to its numerous advantages, including amplitude and frequency stabilization, noise reduction, and sensitivity improvement. However, the limited synchronization bandwidth hinders its broader application, and few techniques have been explored to enhance this aspect. In this paper, we conducted theoretical and experimental studies on the unidirectional synchronization characteristics of a resonator with phase lock loop oscillation. A novel enhancement method for the synchronization bandwidth using a parametrically excited MEMS oscillator is proposed, which achieves a remarkably large synchronization bandwidth of 8.85 kHz, covering more than 94% of the hysteresis interval. Importantly, the proposed method exhibits significant potential for high-order synchronization and frequency stabilization compared to the conventional directly excited oscillator. These findings present an effective approach for expanding the synchronization bandwidth, which has promising applications in nonlinear sensing, fully mechanical frequency dividers, and high-precision time references. [ABSTRACT FROM AUTHOR]

In this paper, a fractional‐order unified system with complex variables is proposed. Firstly, the basic properties of the system including the equilibrium points and symmetry are analyzed. Bifurcations of the system in commensurate‐order and incommensurate‐order cases are studied. Tangent and period‐doubling bifurcations can be observed when a derivative order or a parameter is varied. The stabilization the system is investigated via the predict feedback method. Based on the stability theory of fractional‐order systems, a projective synchronization for the fractional‐order unified complex system is proposed by designing an appropriate controller. Numerical simulations are applied to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena. [ABSTRACT FROM AUTHOR]

We proposed mathematical models for the electrocardiogram and photoplethysmogram signals with functionality to preset the pattern of synchronization between the phases of the low-frequency oscillations, which are related to the sympathetic neuronal control of circulation. The simulated phase difference reproduced the statistical and spectral characteristics of the experimental data, including the alternating horizontal and sloped sections, corresponding to the intervals of synchronous and asynchronous behavior. Using the proposed model, we tested and tuned an algorithm for detection of the phase synchronization between the parts of the sympathetic control of circulation, improving both sensitivity and specificity of the algorithm. [ABSTRACT FROM AUTHOR]

Synchronization is a key feature of the brain dynamics and is necessary for information transmission across brain regions and in higher brain functions like cognition, learning and memory. Experimental findings demonstrated that in cortical microcircuits there are multiple synapses between pairs of connected neurons. Synchronization of neurons in the presence of multiple synaptic connections may be relevant for optimal learning and memory, however, its effect on the dynamics of the neurons is not adequately studied. Here, we address the question that how changes in the strength of the synaptic connections and transmission delays between neurons impact synchronization in a two-neuron system with multiple synapses. To this end, we analytically and computationally investigated synchronization dynamics by considering both phase oscillator model and conductance-based Hodgkin–Huxley (HH) model. Our results show that symmetry/asymmetry of feedforward and feedback connections crucially determines stability of the phase locking of the system based on the strength of connections and delays. In both models, the two-neuron system with multiple synapses achieves in-phase synchrony in the presence of small and large delays, whereas an anti-phase synchronization state is favored for median delays. Our findings can expand the understanding of the functional role of multisynaptic contacts in neuronal synchronization and may shed light on the dynamical consequences of pathological multisynaptic connectivity in a number of brain disorders. [ABSTRACT FROM AUTHOR]

This study explores the impacts of multiple factors (noise, intra-motif coupling, and critical bifurcation parameter) on noise-induced motif synchrony and output regularity in three-node feed-forward-loops (FFLs), distinguishing between coherent FFLs with purely excitatory connections and incoherent FFLs formed by transitioning the intermediate layer to inhibitory connections. Our model utilizes the normal form of Hopf bifurcation (HB), which captures the generic structure of excitability observed in real systems. We find that the addition of noise can optimize motif synchrony and output regularity at the intermediate noise intensities. Our results also suggest that transitioning the excitatory coupling between the intermediate and output layers of the FFL to inhibitory coupling -- i.e., moving from the coherent to the incoherent FFL -- enhances output regularity but diminishes motif synchrony. This shift towards inhibitory connectivity highlights a trade-off between motif synchrony and output regularity and suggests that the structure of the intermediate layer plays a pivotal role in determining the motif's overall dynamics. Surprisingly, we also discover that both motifs achieve their best output regularity at a moderate level of intra-motif coupling, challenging the common assumption that stronger coupling, especially of the excitatory type, results in improved regularity. Our study provides valuable insights into functional differences in network motifs and offers a direct perspective relevant to the field of complex systems as we consider a normal-form model that pertains to a vast number of individual models experiencing HB. [ABSTRACT FROM AUTHOR]

Synchronous dynamics play a pivotal role in various cognitive processes. Previous studies extensively investigate noise-induced synchrony in coupled neural oscillators, with a focus on scenarios featuring uniform noise and equal coupling strengths between neurons. However, real-world or experimental settings frequently exhibit heterogeneity, including deviations from uniformity in coupling and noise patterns. This study investigates noise-induced synchrony in a pair of coupled excitable neurons operating in a heterogeneous environment, where both noise intensity and coupling strength can vary independently. Each neuron is an excitable oscillator, represented by the normal form of Hopf bifurcation (HB). In the absence of stimulus, these neurons remain quiescent but can be triggered by perturbations, such as noise. Typically, noise and coupling exert opposing influences on neural dynamics, with noise diminishing coherence and coupling promoting synchrony. Our results illustrate the ability of asymmetric noise to induce synchronization in such coupled neural oscillators, with synchronization becoming increasingly pronounced as the system approaches the excitation threshold (i.e., HB). Additionally, we find that uneven coupling strengths and noise asymmetries are factors that can promote in-phase synchrony. Notably, we identify an optimal synchronization state when the absolute difference in coupling strengths ismaximized, regardless of the specific coupling strengths chosen. Furthermore, we establish a robust relationship between coupling asymmetry and the noise intensity required to maximize synchronization. Specifically, when one oscillator (receiver neuron) receives a strong input from the other oscillator (source neuron) and the source neuron receives significantly weaker or no input from the receiver neuron, synchrony is maximized when the noise applied to the receiver neuron is much weaker than that applied to the source neuron. These findings reveal the significant connection between uneven coupling and asymmetric noise in coupled neuronal oscillators, shedding light on the enhanced propensity for in-phase synchronization in two-neuron motifs with one-way connections compared to those with two-way connections. This research contributes to a deeper understanding of the functional roles of network motifs that may serve within neuronal dynamics. [ABSTRACT FROM AUTHOR]

Synchronization in microstructures is a widely explored domain due to its diverse dynamic traits and promising practical applications. Within synchronization analysis, the synchronization bandwidth serves as a pivotal metric. While current research predominantly focuses on symmetric evaluations of synchronization bandwidth, the investigation into potential asymmetries within nonlinear oscillators remains unexplored, carrying implications for sensor application performance. This paper conducts a comprehensive exploration employing straight and arch beams capable of demonstrating linear, hardening, and softening characteristics to thoroughly scrutinize potential asymmetry within the synchronization region. Through the introduction of weak harmonic forces to induce synchronization within the oscillator, we observe distinct asymmetry within its synchronization range. Additionally, we present a robust theoretical model capable of fully capturing the linear, hardening, and softening traits of resonators synchronized to external perturbation. Further investigation into the effects of feedback strength and phase delay on synchronization region asymmetry, conducted through analytical and experimental approaches, reveals a consistent alignment between theoretical predictions and experimental outcomes. These findings hold promise in providing crucial technical insights to enhance resonator performance and broaden the application landscape of MEMS (Micro-Electro-Mechanical Systems) technology. [ABSTRACT FROM AUTHOR]

Previous research has delved into the brain's response to top-down and bottom-up conflicts in numerical inductive reasoning. However, the specific neural oscillatory patterns associated with these conflict types in numerical inductive reasoning processing have remained elusive. In this study, we employed a number series completion task in which participants had to determine whether a given target number adhered to concealed rules. Three conditions were established: an identity condition (e.g., 13, 13, 13), a perceptual mismatch condition (representing bottom-up conflict, e.g., 13 13 + 三), and a rule violation condition (representing top-down conflict, e.g., 13 13 14). Our EEG results revealed significant distinctions: rule violation induced more pronounced alpha desynchronization compared to both perceptual mismatch and identity conditions. Conversely, perceptual mismatch was associated with increased theta synchronization in contrast to rule violation and the identity condition. These findings suggest that alpha desynchronization may indicate the integration of rules during top-down conflict, while theta synchronization may function as a mechanism to inhibit bottom-up perceptual interference in numerical inductive reasoning. [ABSTRACT FROM AUTHOR]

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (N P E) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher N P E values than pairs with different degrees. However, large variability is found in the N P E values. Comparing the N P E behavior with that of the phase-locking value (P L V , commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, P L V only displays a monotonic increase, while N P E shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that P L V only captures coupling-induced phase changes, while N P E also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that N P E captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose N P E as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors. [ABSTRACT FROM AUTHOR]

This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range. Such networks compartmentalize the two-dimensional space with no a priori constraints, due to the formation of porous transport walls, and represent a highly complex and novel non-linear behavior. The analysis is numerically carried out as a function of a control parameter showing distinct regimes: static pattern formation, dynamic excitable networks formation, intermittency and chaos. A statistical analysis is drawn to determine the control parameter ranges for the various behaviors to appear. The model and the results shown in this work are expected to contribute to the field of artificial life. [ABSTRACT FROM AUTHOR]

Synchronization is an important phenomenon occurring in many complex systems, such as neural networks, power grids, or social networks. Various methods have been proposed to measure synchronization, each with its advantages and limitations. In this work, we introduce the Poincaré sphere as a generalized measure of synchronization, which provides a useful tool to visualize the similarities between oscillations. We propose the notion of "total synchronization," which considers amplitude, frequency, and phase synchronization, all of which can be measured and visualized simultaneously on the Poincaré sphere. We show that visualizing oscillatory trajectories on the Poincaré sphere has advantages over the more typical two-dimensional representation, particularly in cases where a projection onto a two-dimensional space cannot capture the similarities between different oscillations. Furthermore, we apply this new synchronization measurement to linear and nonlinear oscillators and provide two concrete examples of its application in visualizing phase jitter in noisy oscillations and quantizing solutions of oscillator-based Ising machines. Our work demonstrates the usefulness of the Poincaré sphere as a generalized measure of synchronization and provides a new perspective on studying synchronization in complex systems. [ABSTRACT FROM AUTHOR]

At present, inverted pendulum model (IPM) has been recognized by increasing researchers due to its capability to capture the characteristics of pedestrian lateral excitation. However, the IPM still has a downside that has been continuously questioned: the velocity proportional pedestrian load coefficient c p is inconsistent with the on-site observations in the case of pedestrian walking with normal frequency. This problem is most likely resulted from that the IPM ignores the synchronization effect. The IPM is derived from indoor single-person experiment and cannot consider the synchronization in the crowd. Synchronization effects are classified into two types： pedestrian–bridge and pedestrian–pedestrian synchronizations. Pedestrian–bridge synchronization is stimulated by bridge vibration, whereas pedestrian–pedestrian synchronization is stimulated by surrounding crowd. In this study, a novel model for pedestrian-induced lateral vibration of footbridge is proposed. It uses the IPM as the basis and adopts a binary coupled Kuramoto model that originally derived from the collective synchronization phenomena to overcome the limitation in IPM. This model can consider the pedestrian–bridge and pedestrian–pedestrian synchronizations, which provides a new way to reveal the mechanism of pedestrian-induced lateral vibration of footbridge. The proposed method is verified through a case study of the London Millennium Bridge, and some useful conclusions are obtained. [ABSTRACT FROM AUTHOR]

Wind tunnel experiments are performed on a pitch-plunge aeroelastic system possessing structural nonlinearity in the stiffness and subjected to dynamic stall conditions. With an increase in the flow speed (U), we observe a well-expected transition from decaying responses to limit cycle oscillations wherein the flutter frequencies of pitch and plunge coalesce perfectly close to the pitch natural frequency, indicating the onset of stall flutter. Interestingly, a further increase in the U yields a secondary frequency peak, emerging approximately at half of the primary frequency peak, accompanied by an intermittent period-1–period-2 (P1–P2) behaviour. Another transition is observed as the flow speed is increased further—the pitch-plunge motion starts exhibiting a beat-like response. We demonstrate that this particular behaviour is '2:1 internal resonance (IR)' and is attributed to a specific combination of structural parameters: the ratio ( ω ¯ ) of natural frequencies of plunge and pitch ( f y and f α , respectively) being 0.44, and the structure possessing quadratic nonlinearity, resulting as the aerodynamic loads tune the flutter frequencies to become commensurate for a 2:1 IR. We show that a typical phase synchronization analysis is inadequate to explain the atypical transitions. To that end, we resort to a frequency-specific synchronization analysis wherein the pitch and plunge time signals are decomposed into two signals of specific frequency range. This reveals that the higher frequency signal (HFS) is always perfectly synchronized. On contrary, the lower frequency signal (LFS) is asynchronous during the intermittent regime and has strong synchrony at the onset of beats. The physical insights presented in this study can be useful for the design of increasingly slender aeroelastic structures that are often subjected to dynamic stall. [ABSTRACT FROM AUTHOR]

Herein, we provide a brief overview of complex systems theory approaches to investigate the genomic mechanism of cell-fate changes. Cell trajectories across the epigenetic landscape, whether in development, environmental responses, or disease progression, are controlled by extensively coordinated genome-wide gene expression changes. The elucidation of the mechanisms underlying these coherent expression changes is of fundamental importance in cell biology and for paving the road to new therapeutic approaches. In previous studies, we pointed at dynamic criticality as a plausible characteristic of genome-wide transition dynamics guiding cell fate. Whole-genome expression develops an engine-like organization (genome engine) in order to establish an autonomous dynamical system, capable of both homeostasis and transition behaviors. A critical set of genes behaves as a critical point (CP) that serves as the organizing center of cell-fate change. When the system is pushed away from homeostasis, the state change that occurs at the CP makes local perturbation spread over the genome, demonstrating self-organized critical (SOC) control of genome expression. Oscillating-Mode genes (which normally keep genome expression on pace with microenvironment fluctuations), when in the presence of an effective perturbative stimulus, drive the dynamics of synchronization, and thus guide the cell-fate transition. [ABSTRACT FROM AUTHOR]

Absence seizures--generalized rhythmic spike-and-wave discharges (SWDs) are the defining property of childhood (CAE) and juvenile (JAE) absence epilepsies. Such seizures are the most compelling examples of pathological neuronal hypersynchrony. All the absence detection algorithms proposed so far have been derived from the properties of individual SWDs. In this work, we investigate EEG phase synchronization in patients with CAE/JAE and healthy subjects to explore the possibility of using the wavelet phase synchronization index to detect seizures and quantify their disorganization (fragmentation). The overlap of the ictal and interictal probability density functions was high enough to preclude effective seizure detection based solely on changes in EEG synchronization. We used a machine learning classifier with the phase synchronization index (calculated for 1 s data segments with 0.5 s overlap) and the normalized amplitude as features to detect generalized SWDs. Using 19 channels (10-20 setup), we identified 99.2% of absences. However, the overlap of the segments classified as ictal with seizures was only 83%. The analysis showed that seizures were disorganized in approximately half of the 65 subjects. On average, generalized SWDs lasted about 80% of the duration of abnormal EEG activity. The disruption of the ictal rhythm can manifest itself as the disappearance of epileptic spikes (with high-amplitude delta waves persisting), transient cessation of epileptic discharges, or loss of global synchronization. The detector can analyze a real-time data stream. Its performance is good for a six-channel setup (Fp1, Fp2, F7, F8, O1, O2), which can be implemented as an unobtrusive EEG headband. False detections are rare for controls and young adults (0.03% and 0.02%, respectively). In patients, they are more frequent (0.5%), but in approximately 82% cases, classification errors are caused by short epileptiform discharges. Most importantly, the proposed detector can be applied to parts of EEGwith abnormal EEGactivity to quantitatively determine seizure fragmentation. This property is important because a previous study reported that the probability of disorganized discharges is eight times higher in JAE than in CAE. Future research must establish whether seizure properties (frequency, length, fragmentation, etc.) and clinical characteristics can help distinguish CAE and JAE. [ABSTRACT FROM AUTHOR]

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization. [ABSTRACT FROM AUTHOR]

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type. [ABSTRACT FROM AUTHOR]

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, while how the system is steering toward different final destinies upon spatially localized perturbation is still unknown. Through a systematic numerical analysis of the evolution of the spatiotemporal patterns of multi-chimera states, we uncover a critical behavior of the system in transient time toward either chimera or synchronization as the final stable state. We measure the critical values and the transient time of chimeras with different numbers of clusters. Then, based on an adequate verification, we fit and analyze the distribution of the transient time, which obeys power-law variation process with the increase in perturbation strengths. Moreover, the comparison between different clusters exhibits an interesting phenomenon, thus we find that the critical value of odd and even clusters will alternatively converge into a certain value from two sides, respectively, implying that this critical behavior can be modeled and enabling the articulation of a phenomenological model. [ABSTRACT FROM AUTHOR]

Synchronization of two or more self-sustained oscillators is a well-known and studied phenomenon, appearing both in natural and designed systems. In some cases, the synchronized state is undesired, and the aim is to destroy synchrony by external intervention. In this paper, we focus on desynchronizing two self-sustained oscillators by short pulses delivered to the system in a phase-specific manner. We analyze a non-trivial case when we cannot access both oscillators but stimulate only one. The following restriction is that we can monitor only one unit, be it a stimulated or non-stimulated one. First, we use a system of two coupled Rayleigh oscillators to demonstrate how a loss of synchrony can be induced by stimulating a unit once per period at a specific phase and detected by observing consecutive inter-pulse durations. Next, we exploit the phase approximation to develop a rigorous theory formulating the problem in terms of a map. We derive exact expressions for the phase–isostable coordinates of this coupled system and show a relation between the phase and isostable response curves to the phase response curve of the uncoupled oscillator. Finally, we demonstrate how to obtain phase response information from the system using time series and discuss the differences between observing the stimulated and unstimulated oscillator. [ABSTRACT FROM AUTHOR]

Rationalized development of electrical stimulation (ES) therapy is of paramount importance. Not only it will foster new techniques and technologies with increased levels of safety, efficacy, and efficiency, but it will also facilitate the translation from basic research to clinical practice. For such endeavor, design of new technologies must dialogue with state-of-the-art neuroscientific knowledge. By its turn, neuroscience is transitioning--a movement started a couple of decades earlier--into adopting a new conceptual framework for brain architecture, in which time and thus temporal patterns plays a central role in the neuronal representation of sampled data from the world. This article discusses how neuroscience has evolved to understand the importance of brain rhythms in the overall functional architecture of the nervous system and, consequently, that neuromodulation research should embrace this new conceptual framework. Based on such support, we revisit the literature on standard (fixed-frequency pulsatile stimuli) and mostly non-standard patterns of ES to put forward our own rationale on how temporally complex stimulation schemes may impact neuromodulation strategies. We then proceed to present a low frequency, on average (thus low energy), scale-free temporally randomized ES pattern for the treatment of experimental epilepsy, devised by our group and termed NPS (Non-periodic Stimulation). The approach has been shown to have robust anticonvulsant effects in different animal models of acute and chronic seizures (displaying dysfunctional hyperexcitable tissue), while also preserving neural function. In our understanding, accumulated mechanistic evidence suggests such a beneficial mechanism of action may be due to the natural-like characteristic of a scale-free temporal pattern that may robustly compete with aberrant epileptiform activity for the recruitment of neural circuits. Delivering temporally patterned or random stimuli within specific phases of the underlying oscillations (i.e., those involved in the communication within and across brain regions) could both potentiate and disrupt the formation of neuronal assemblies with random probability. The usage of infinite improbability drive here is obviously a reference to the "The Hitchhiker's Guide to the Galaxy" comedy science fiction classic, written by Douglas Adams. The parallel is that dynamically driving brain functional connectogram, through neuromodulation, in a manner that would not favor any specific neuronal assembly and/or circuit, could re-stabilize a system that is transitioning to fall under the control of a single attractor. We conclude by discussing future avenues of investigation and their potentially disruptive impact on neurotechnology, with a particular interest in NPS implications in neural plasticity, motor rehabilitation, and its potential for clinical translation. [ABSTRACT FROM AUTHOR]

Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types. [ABSTRACT FROM AUTHOR]

In this work a master-slave configuration to obtain synchronization between the double-well Duffing-van der Pol (master system) and the three-well Φ6 Duffing oscillators (slave system) is studied. For this configuration, we analyze the system when the dissipative and one that combines the elastic and dissipative couplings are used. Whenever the dissipative coupling is used, we observed a vertical shift synchronization in the slave system. However, when the combination of the elastic and dissipative couplings is used, the vertical shift disappears obtaining complete synchronization. We resort to perturbation method to corroborate analytically these kind of synchronization, when the master system provides an harmonic function to the slave system. These synchronizations are numerically corroborated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this study, we introduce a design of a feedback-type fluidic oscillator with elastic structures surrounding its feedback channel. By employing phase reduction theory, we extract the phase sensitivity function of the complex fluid–structure coupled system, which represents the system's oscillatory characteristics. We show that the frequency of the oscillating flow inside the fluidic oscillator can be modulated by inducing synchronization with the weak periodic forcing from the elastic structure vibration. This design approach adds controllability to the fluidic oscillator, where conventionally, the intrinsic oscillatory characteristics of such device were highly determined by its geometry. The synchronization-induced control also changes the physical characteristics of the oscillatory fluid flow, which can be beneficial for practical applications, such as promoting better fluid mixing without changing the overall geometry of the device. Furthermore, by analyzing the phase sensitivity function, we demonstrate how the use of phase reduction theory gives good estimation of the synchronization condition with minimal number of experiments, allowing for a more efficient control design process. Finally, we show how an optimal control signal can be designed to reach the fastest time to synchronization. [ABSTRACT FROM AUTHOR]

The Winfree model is a phase-coupled synchronization model which simplifies pulse-coupled models such as the Peskin model on pacemaker cells. It is well-known that the Winfree ensemble with the first-order coupling exhibits discrete asymptotic patterns such as incoherence, locking and death depending on the coupling strength and variance of natural frequencies. In this paper, we further study higher-order couplings which makes the dynamics more close to the behaviors of the Peskin model. For this, we propose several sufficient frameworks for asymptotic patterns compared to the first-order coupling model. Our proposed conditions on the coupling strength, natural frequencies and initial data are independent of the number of oscillators so that they can be applied to the corresponding mean-field model. We also provide several numerical simulations and compare them with analytical results. [ABSTRACT FROM AUTHOR]

The inhomogeneous population distribution appears as various population densities or different types of dynamics in distant sites of the extended habitat and may arise due to, for example, the resettlement features, the internal population structure, and the population dynamics synchronization mechanisms between adjacent subpopulations. In this paper, we propose the model of the spatio-temporal dynamics of two-age-structured populations coupled by migration (metapopulation) with long-range displacement. We study mechanisms leading to inhomogeneous spatial distribution as a type of cluster synchronization of population dynamics. To study the spatial patterns and synchronization, we use the method of constructing spatio-temporal profiles and spatial return maps. We found that patterns with spots or stripes are typical spatial structures with synchronous dynamics. In most cases, the spatio-temporal dynamics are mixed with randomly located single populations with strong burst (outbreak) of population size (solitary states). As the coupling parameters decrease, the number of solitary states grows, and they increasingly synchronize and form the clusters of solitary states. As a result, there are the several clusters with different dynamics. The appearance of these spatial patterns most likely occurs due to the multistability of the local age-structured population, leading to the spatio-temporal multistability. [ABSTRACT FROM AUTHOR]

Synchronization plays a key role in learning and memory by facilitating the communication between neurons promoted by synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity that modifies the strength of synaptic connections between neurons based on the coincidence of pre- and postsynaptic spikes. In this way, STDP simultaneously shapes the neuronal activity and synaptic connectivity in a feedback loop. However, transmission delays due to the physical distance between neurons affect neuronal synchronization and the symmetry of synaptic coupling. To address the question that how transmission delays and STDP can jointly determine the emergent pairwise activity-connectivity patterns, we studied phase synchronization properties and coupling symmetry between two bidirectionally coupled neurons using both phase oscillator and conductance-based neuron models. We show that depending on the range of transmission delays, the activity of the two-neuron motif can achieve an in-phase/anti-phase synchronized state and its connectivity can attain a symmetric/asymmetric coupling regime. The coevolutionary dynamics of the neuronal system and the synaptic weights due to STDP stabilizes the motif in either one of these states by transitions between in-phase/anti-phase synchronization states and symmetric/asymmetric coupling regimes at particular transmission delays. These transitions crucially depend on the phase response curve (PRC) of the neurons, but they are relatively robust to the heterogeneity of transmission delays and potentiation-depression imbalance of the STDP profile. [ABSTRACT FROM AUTHOR]

A detailed study of the characteristics of the time-delay signature of a single loop optoelectronic oscillator incorporating a nonlinear amplifier of sine hyperbolic type is presented. We demonstrate that with appropriate values of the system parameters, the unique time-delay of the system cannot be traced in its dynamics. Such an advantage is exploited in synchronization using a scheme that confirms the use of the hidden time-delay as a key. Furthermore, a new tunable parameter which may serve as a key in a secure communication scheme arises as a result of the introduction of the nonlinear amplifier. We expect this system to emulate a general benefit in the physical equipment, and reduce their cost and congestion. [ABSTRACT FROM AUTHOR]

Previous single-brain studies suggested interoception plays a role in interpersonal synchronization. The aim of the present study was to assess the electrophysiological intersubject coherence through electrophysiological (EEG) hyperscanning recording during simple dyadic synchronization tasks when the participants focused on their breath. To this aim, the neural activity of 15 dyads of participants was collected during the execution of a cognitive and motor synchronization task in two distinct IA conditions: focus and no focus on the breath condition. Individuals' EEG frequency bands were recorded through EEG hyperscanning and coherence analysis was performed. Results showed greater EEG coherence was observed for the alpha band in frontopolar brain regions (Fp1, Fp2) and also in central brain regions (C3, C4) within the dyads, during the focus on the breath condition for the motor compared to the cognitive synchronization task; during the same experimental condition, delta and theta band showed augmented inter-individual coherence in the frontal region (Fz) and central areas (C3, C4). To conclude, the current hyperscanning study highlights how the manipulation of the interoceptive focus (obtained through the focus on the breath) strengthens the manifestation of the EEG markers of interpersonal tuning during a motor synchronization task in specific brain areas. [ABSTRACT FROM AUTHOR]

Synchronous stability in power systems is of essential importance for system safety and operation. For the phase-locked loop (PLL)-based synchronous stability in power electronic-based power systems, which has recently stimulated interest in researchers in the field of electrical power engineering, but is still controversial, this paper divides the topic into two aspects, including the PLL device stability and the system stability. It is found that the PLL device is always stable and the error between the PLL output angle θ p l l and the terminal voltage angle θ t is always finite. Therefore, the synchronization of power electronic-based power systems should be understood as the output synchronization between the electrical rotation vectors ( θ t or θ p l l ) from each item of grid-tied equipment, rather than the synchronization of the PLL device itself. In addition, it is found that θ p l l plays an active role in the system synchronization dynamics not only in electromagnetic timescales but also electromechanical timescales and it could be selected as a dominant observable. In this paper, the concept of synchronous stability is well clarified. These findings are well supported by theoretical analyses and MATLAB/Simulink simulations, and thus could provide insights on the synchronous stability mechanism. [ABSTRACT FROM AUTHOR]

Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences. [ABSTRACT FROM AUTHOR]

Perception-action coordination (also known as sensorimotor synchronization, SMS) is often studied by analyzing motor coordination with auditory rhythms. The current study assesses phasing—a compositional technique in which two people tap the same rhythm at varying phases by adjusting tempi—to explore how SMS is impacted by individual and situational factors. After practice trials, participants engaged in the experimental phasing task with a metronome at tempi ranging from 80–140 beats per minute (bpm). Multidimensional recurrence quantification analysis (MdRQA) was used to compare nonlinear dynamics of phasing performance. Varying coupling patterns emerged and were significantly predicted by tempo and linguistic experience. Participants who successfully phased replicated findings from an original case study, demonstrating stable tapping patterns near in-phase and antiphase, while those unsuccessful at phasing showed weaker attraction to in-phase and antiphase. [ABSTRACT FROM AUTHOR]

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order to fill this gap, we present a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. This phenomenon is manifested at the macroscopic level by temporal episodes of coherent and incoherent dynamics that alternate recurrently. At the same time, the dynamics of the individual nodes do not change qualitatively. We identify asymmetric adaptation rules and temporal separation between the adaptation and the dynamics of individual nodes as key features for the emergence of recurrent synchronization. Our results suggest that asymmetric adaptation might be a fundamental ingredient for recurrent synchronization phenomena as seen in pattern generators, e.g., in neuronal systems. [ABSTRACT FROM AUTHOR]