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The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations. [ABSTRACT FROM AUTHOR]

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]

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]

Coherent terahertz (THz) radiations based on intrinsic Josephson junctions (IJJs) from a Bi2Sr2CaCu2O (BSCCO) mesa under a bias voltage were observed in 2007. Later on, a novel phase kink state was proposed which can explain the key experimental results. However, how to drive the system into the phase kink state efficiently still remains an open problem. In this work, we propose several ways to synchronize the system to the phase kink state. We start from random and typical regular initial phase configurations. It is found that starting from some initial phase configurations, the system can be driven efficiently into the phase kink state. The time spent before entering the phase kink states for these initial phase configurations is shorter when the initial phase configuration is further away from the uniform phase configuration. [ABSTRACT FROM AUTHOR]

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference δϕ between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index γ = ⟨sinΔϕ⟩² + ⟨cosδϕ⟩² that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index γ has two distinct peaks, one at 0.11 Hz [γ = 0.59 ± 0.09] and another at 0.33 Hz (γ = 0.55 ± 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this pan of the spectrum is equal to 0.13 ± 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced. [ABSTRACT FROM AUTHOR]

One of the most sensitive methods for determining the presence and character of coupling between two oscillators is based on the modeling of their phase dynamics. This method is applicable if the observed oscillations are not synchronous and the length of available time series is no less than 50 characteristic periods. Now it is established that the method can be applied to still shorter time series with a length of 20 to 50 periods, provided that the estimated phase coherence coefficient (measuring the degree of synchronization) does not exceed a certain threshold dependent on the time series length and the frequency detuning. This result expands the possibilities of detecting the coupling between oscillatory systems under conditions of nonstationary signals and deficient data. [ABSTRACT FROM AUTHOR]

Complex-valued Hopfield networks which possess the energy function are analyzed. The dynamics of the network with certain forms of an activation function is decomposable into the dynamics of the amplitude and phase of each neuron. Then the phase dynamics is described as a coupled system of phase oscillators with a pair-wise sinusoidal interaction. Therefore its phase synchronization mechanism is useful for the area-wide offset control of the traffic signals. The computer simulations show the effectiveness under the various traffic conditions. [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]

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]

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 investigate theoretically and experimentally the detrimental effect of fiber dispersion on the synchronization of an optoelectronic phase chaos cryptosystem. We evaluate the root-mean square synchronization error and the cancellation spectra between the emitter and the receiver in order to characterize the quality of the optical fiber communication link. These two indicators explicitly show in temporal and spectral domain how fiber dispersion does negatively affect the phase chaos cancellation at the receiver stage. We demonstrate that the dispersion management techniques used in conventional optical fiber networks, such as dispersion-compensating modules/fibers or dispersion shifted fibers, are also efficient to strongly reduce the detrimental effects of fiber propagation in phase chaos communications. This compatibility therefore opens the way to a successful integration of more than 10-Gb/s phase chaos communications systems in existing networks, even when the fiber link spans over more than 100 km. [ABSTRACT FROM PUBLISHER]

A new method is proposed for the investigation of transitions from synchronous dynamics of coupled oscillators to asynchronous regimes attained upon synchronization breakage by a sequence of short phase resetting pulses. The possibility to use the proposed method for determining the coefficient of coupling between interacting systems from an analysis of the signals generated by these systems is considered. [ABSTRACT FROM AUTHOR]

In this paper we extend the results of Frankel and Kiemel [SIAM J. Appl. Math, 53 (1993), pp. 1436-1446] to a network of slowly coupled oscillators. First, we use Malkin's theorem to derive a canonical phase model that describes synchronization properties of a slowly coupled network. Then, we illustrate the result using slowly coupled oscillators (1) near Andronov-Hopf bifurcations, (2) near saddle-node on invariant circle bifurcations, and (3) near relaxation oscillations. We compare and contrast synchronization properties of slowly and weakly coupled oscillators. [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 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]

Summary: Control‐channel interactions in a linear diffusive network model are studied, with the aim of determining the role of the network's topology in such interactions. Specifically, the influence of a built controller on the infinite and finite zero structure of a second control channel is characterized. The analysis shows how the network's graph topology, the relative positions of the two channels, and the architecture of the built controller influence the zero structure of the second control channel. Further, the influence of low or high gain controller designs on remote channels is examined. The analyses demonstrate that some control architectures and positions can introduce undesirable nonminimum‐phase dynamics at remote locations, while others are guaranteed to maintain or promote minimum‐phase dynamics. [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]

We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases. [ABSTRACT FROM AUTHOR]

We studied the properties of low-frequency (LF) heart rate variability (HRV) and photoplethysmographic waveform variability (PPGV) and their interaction under conditions where the hemodynamic connection between them is obviously absent, as well as the LF regulation of PPGV in the absence of heart function. The parameters of HRV and finger PPGV were evaluated in 10 patients during cardiac surgery under cardiopulmonary bypass (on-pump cardiac surgery) with or without cardioplegia. The following spectral indices of PPGV and HRV were ertimated: the total spectral power (TP), the high-frequency (HF) and the LF ranges of TP in percents (HF% and LF%), and the LF/HF ratio. We assessed also the index S of synchronization between the LF oscillations in finger photoplethysmogram (PPG) and heart rate (HR) signals. The analysis of directional couplings was carried out using the methods of phase dynamics modeling. It is shown that the mechanisms leading to the occurrence of oscillations in the LF range of PPGV are independent of the mechanisms causing oscillations in the LF range of HRV. At the same time, the both above-mentioned LF oscillations retain their activity under conditions of artificial blood circulation and cardioplegia (the latter case applies only to LF oscillations in PPG). In artificial blood circulation, there was a coupling from the LF oscillations in PPG to those in HR, whereas the coupling in the opposite direction was absent. The coupling from the LF oscillations in PPG to those in HR has probably a neurogenic nature, whereas the opposite coupling has a hemodynamic nature (due to cardiac output). [ABSTRACT FROM AUTHOR]

We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach. [ABSTRACT FROM AUTHOR]

We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized. [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]

The role of the phase dynamics in turbulence is investigated. As a demonstration of the importance of the phase dynamics, a simplified system is used, namely the one-dimensional Burgers equation, which is evolved numerically. The system is forced via a known external force, with two components that are added into the evolution equations of the amplitudes and the phase of the Fourier modes, separately. In this way, we are able to control the impact of the force on the dynamics of the phases. In the absence of the direct forcing in the phase equation, it is observed that the phases are not stochastic as assumed in the Random Phase Approximation (RPA) models, and in contrast, the non-linear couplings result in intermittent locking of the phases to ± π/2. The impact of the force, applied purely on the phases, is to increase the occurrence of the phase locking events in which the phases of the modes in a wide k range are now locked to ± π/2, leading to a change in the dynamics of both phases and amplitudes, with a significant localization of the real space flow structures. [ABSTRACT FROM AUTHOR]

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for antiphase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. [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]

Synchronization properties of model systems containing large numbers of phase oscillators have many potential biophysical and other applications. Biophysical examples include networks of pacemaker cells in the heart and suprachiasmatic nucleus of the brain. In physical systems, the phase dynamics of high-Tc superconducting materials continue to attract attention, since systems of intrinsic Josephson junctions form natural arrays of coupled phase oscillators. As such, they have the potential to act as systems in which various exotic synchronization effects may be observed. In this paper, we make a more detailed exploration of the parameter space containing regions of spontaneous chaos synchronization in the CCJJ + DC model of intrinsic Josephson junctions. Extensive regions of phase synchronization-corresponding to the Shapiro steps with zero charge density in the S-layers-are found through numerical simulation. By computing the Lyapunov exponent spectra, we see that the spontaneous chaos synchronization occurs within certain subregions that overlap with uncharged steps in the IV-characteristics. We tried to stabilize the spontaneous chaos synchronization over a wider range of parameters, by applying a global, noninvasive, and proportional control scheme. The control is affected by applying a time-dependent phase shift to the external electromagnetic radiation, proportional to the total voltage. The effect of the control is found to be three-fold. First, it tends to broaden the current interval over which lower harmonic Shapiro steps occur. Second, it does not change the width in the current range over which the chaos synchronization occurs. Third, it makes the chaos synchronization more robust to thermal noise. The chaos synchronization we report here may be useful in any applications requiring more powerful, high-frequency, and chaotic signals, such as in secure communication. [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]

Noise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms. [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]