Synchronous State Research Articles

Higher-order interaction induced chimeralike state in a bipartite network.

We report higher-order coupling induced stable chimeralike state in a bipartite network of coupled phase oscillators without any time-delay in the coupling. We show that the higher-order interaction breaks the symmetry of the homogeneous synchronized state to facilitate the manifestation of symmetry breaking chimeralike state. In particular, such symmetry breaking manifests only when the pairwise interaction is attractive and higher-order interaction is repulsive, and vice versa. Further, we also demonstrate the increased degree of heterogeneity promotes homogeneous symmetric states in the phase diagram by suppressing the asymmetric chimeralike state. We deduce the low-dimensional evolution equationsfor the macroscopic order parameters using Ott-Antonsen ansatz and obtain the bifurcation curves from them using the software xppaut, which agrees very well with the simulation results. We also deduce the analytical stability conditions for the incoherent state, in-phase and out-of-phase synchronized states, which match with the bifurcation curves.

Synchronization Control of Complex Spatio-Temporal Networks Based on Fractional-Order Hyperbolic PDEs with Delayed Coupling and Space-Varying Coefficients

This paper studies synchronization behaviors of two sorts of non-linear fractional-order complex spatio-temporal networks modeled by hyperbolic space-varying PDEs (FCSNHSPDEs), respectively, with time-invariant delays and time-varying delays, including one delayed coupling. One distributed controller with space-varying control gains is firstly designed. For time-invariant delayed cases, sufficient conditions for synchronization of FCSNHSPDEs are presented via LMIs, which have no relation to time delays. For time-varying delayed cases, synchronization conditions of FCSNHSPDEs are presented via spatial algebraic LMIs (SALMIs), which are related to time delay varying speeds. Finally, two examples show the validity of the control approaches.

Dynamic Characteristics Analysis of the DI-SO Cylindrical Spur Gear System Based on Meshing Conditions

The dual-input single-output (DI-SO) cylindrical spur gear system possesses advantages such as high load-carrying capacity, precise transmission, and low energy loss. It is increasingly becoming a core component of power transmission systems in maritime vessels, aerospace, marine engineering, and construction machinery. In practical operation, the stability of the DI-SO cylindrical spur gear system is influenced by complex excitations. These excitations lead to nonlinear vibration, meshing instability, and noise, which affect the performance and reliability of the entire equipment. Hence, the dynamic performance of the DI-SO cylindrical spur gear system is thoroughly investigated in this research. The impact of excitations and nonlinear factors on the dynamic characteristics was investigated comprehensively. A comparative analysis of the gear system was conducted by establishing a bending–torsional coupling vibration analysis model under synchronous and asynchronous meshing conditions. Nonlinear factors such as periodic time-varying meshing stiffness, meshing damping, friction coefficient, friction arms, load sharing ratio, comprehensive transmission error, and backlash were considered in the proposed model. Then, the effect laws of excitations and nonlinear factors such as meshing frequency, driving load fluctuation, backlash, and comprehensive transmission error were analyzed. The results indicate that the dynamic characteristics exhibited staged stable and unstable states under different meshing frequencies and meshing conditions. At the medium-frequency meshing stage (0.96 × 104~1.78 × 104 Hz), alternating phenomena of multi-periodic, quasi-periodic, and chaotic motion states were observed. Moreover, the root mean square value (RMS) of the dynamic transmission error (DTE) in the asynchronized gear system was generally higher than that in the synchronized gear system. It was found that selecting the appropriate meshing condition could effectively reduce the amplitude of the DTE. Additionally, the dynamic performance could be significantly improved by adjusting control parameters such as driving load fluctuation (0~179 N), backlash (0.8 × 10−4~0.9 × 10−4 m), and comprehensive transmission error (7.9 × 10−4~9.4 × 10−4 m). The research results provide a theoretical guidance for the design and optimization of the DI-SO cylindrical spur gear system.

Synchronization processes in fNIRS visibility networks

We employ Kuramoto model to assess the presence of synchronization in individuals who fulfill a cooperation task. Our input data is a couple of signals obtained from functional Near-Infrared Spectroscopy Data Acquisition and Pre-processing technology that is used to capture the brain activity of an individual by measuring the oxyhemoglobin (HbO) level. We consider 1 min signal for individuals in three distinct states: (i) rest; (ii) before a disturb happens; (iii) after the disturbance. We estimate global and local order parameters synchronization with the purpose to compare the conditions of reaching a synchronous state in the networks corresponding to different states for distinct individuals and hemispheres of the prefrontal cortices of same individual. Experimental results confirmed once more that coherent state is reached not for same conditions in both individuals and hemispheres of the prefrontal cortices. Furthermore, condition changes even for different events. The computation of the effective frequencies for each degree class indicates clearly the network difference in rest, before and after disturb. Finally, we investigate the dynamic connectivity matrix and consider the similarity between distinct prefrontal cortices over time.

Recovery of synchronized oscillations on multiplex networks by tuning dynamical time scales

The heterogeneity among interacting dynamical systems or variations in the pattern of their interactions occur naturally in many real complex systems. Often they lead to partially synchronized states like chimeras or oscillation suppressed states like in-homogeneous or homogeneous steady states. In such cases, it is a challenge to get synchronized oscillations in spite of prevailing heterogeneity. In this study, we present a formalism for controlling multi layer, multi timescale systems and show how synchronized oscillations can be restored by tuning the dynamical time scales between the layers. Specifically, we use the model of a multiplex network, where the first layer of coupled oscillators is multiplexed with an environment layer, that can generate various types of chimera states and suppressed states. We show that by tuning the time scale mismatch between the layers, we can revive the synchronized oscillations. We analyse the nature of the transition of the system to synchronization from various dynamical states and the role of time scale mismatch and strength of inter layer coupling in this scenario. We also consider a three-layer multiplex system, where two system layers interact with the common environment layer. In this case, we observe anti synchronization and in-homogeneous steady states on the system layers and by tuning their time scale difference with the environment layer, they undergo transition to synchronized oscillations.

Evaluating Drawings’ Creativity: Synchrony Effects on Rater Bias and the Mediating Role of Emotional Arousal

ABSTRACT Creativity evaluation, particularly rating the creativity of products, is an unstable construct subjective to the influence of various individual states and characteristics. However, little research has been conducted on whether and how participants’ physiological states affect rating products. This experimental study aimed to explore how synchrony (i.e. whether individuals’ evaluation time synchronizes with their peak circadian arousal periods during a day) affects the rating of creativity in drawings, whether these effects vary according to drawings’ different creativity levels, and the influence of emotional state on synchrony and creativity rating. A sample of 191 university students rated several drawings of low, medium, and high creativity levels at their optimal or non-optimal times of day, and their subjective emotional valence and arousal were recorded. The results showed that participants exhibited a more positive rater bias when rating low- and medium-creativity-level drawings during their optimal times of day. Emotional arousal, but not valence, mediated the relationship between synchrony and rater bias. These findings highlight the role of synchrony and emotional arousal in rating creative products, contributing to our understanding of how raters’ synchrony states influence creativity evaluation.

Predefined-time synchronization of time-varying delay fractional-order Cohen–Grossberg neural network based on memristor

This paper delves into the synchronization dynamics of fractional-order memristor Cohen–Grossberg neural network systems with time-varying delays at predefined times (PTS-MFCGNNs). Firstly, leveraging the concept of predefined-time stability, we devise a fractional-order controller, establish sufficient conditions for predefined-time synchronization, and achieve synchronization within the Cohen–Grossberg drive–response system. Secondly, building upon these findings, we scrutinize the synchronization dynamics within the time domain of the PTS-MFCGNNs system. Finally, we validate our theoretical framework through numerical simulations and engage in a comprehensive discussion on predefined-time synchronization within the PTS-MFCGNNs system.

Studies on multi-frequency synchronization of two pairs of counter-rotating exciters in a split drive double-body vibrating system

In this article, the multi-frequency synchronization characteristics and stability of a split drive double-body vibrating system with two rigid frames (RFs), driven by two pairs of counter-rotating exciters symmetrically mounted on two different RFs, are investigated in detail by theory, numeric, and simulation. Based on Lagrange’s equations, the differential equations of motion of the system are deduced. The theoretical criteria for implementing foundation frequency, double-frequency, and triple-frequency synchronization of two pairs of exciters are obtained by applying the asymptotic method. The stability criteria of the synchronous states are derived according to the Routh–Hurwitz criterion. Then, the synchronous and stable regions and stability ability coefficients of the system are analyzed qualitatively by numeric. The simulations are conducted to verify the validity of the theoretical methods used and the correctness of corresponding theoretical results. It is shown that, under the precondition of realizing the multi-frequency synchronization, the ideal working point of the system should be set in Region I to obtain the larger and more stable superposition vibration amplitude between two RFs in engineering. The present work can provide theory guidance for designing new types of vibrating equipment with two different driving frequencies.

Synchronization of high-dimensional Kuramoto-oscillator networks with variable-gain impulsive coupling on the unit sphere

Kuramoto models (KMs) in scalar or high-dimensional form can describe the synchronization phenomenon for large populations of coupled oscillators in networks of dynamical systems such as power grids, satellite mobile sensing networks, etc. However, these models are developed based on continuous-time coupling among oscillators, which is not applicable to networks where the coupling between oscillators occurs only at impulsive instants. Herein, we propose for the first time a generalized high-dimensional Kuramoto oscillator network (HDKON) with variable-gain impulsive coupling on the unit sphere. The proposed HDKON can be reduced to a scalar form comprising a sinusoidal function, thereby generalizing the scalar KM in both temporal and spatial domains. Furthermore, we provide some variation coefficients of the synchronization errors for the oscillator pairs at impulsive instants, and derive a sufficient condition for the exponential synchronization of the HDKON with identical natural frequency. Moreover, we consider an HDKON with a central oscillator and demonstrate that peripheral oscillators almost globally exponentially synchronize to the central oscillator under a sufficient condition. Finally, numerical simulations are performed to verify the main theoretical results.

Aperiodic intermittent dynamic event-triggered synchronization control for stochastic delayed multi-links complex networks

In this work, the exponential synchronization issue of stochastic complex networks with time delays and time-varying multi-links (SCNTM) is discussed via a novel aperiodic intermittent dynamic event-triggered control (AIDE-TC). The AIDE-TC is designed by combining intermittent control with an exponential function and dynamic event-triggered control, aiming to minimize the number of the required triggers. Then, based on the proposed control strategy, the sufficient conditions for exponential synchronization in mean square of SCNTM are obtained by adopting graph theoretic approach and Lyapunov function method. In the meanwhile, it is proven that the Zeno behavior can be excluded under the AIDE-TC, which ensures the feasibility of the control mechanism to realize the synchronization of SCNTM. Finally, we provide a numerical simulation on islanded microgrid systems to validate the effectiveness of main results and the simulation comparison results show that the AIDE-TC can reduce the number of event triggers.

Secure pinning synchronization on aperiodic intermittent event-triggered control in discrete-time complex networks against multi-pattern link attacks

This paper investigates the problem of secure synchronization in aperiodic intermittent event-triggered pinning control for discrete-time complex networks (DCNs) against multi-pattern link attacks. Firstly, in order to reduce communication burden and control cost, a novel aperiodic intermittent event-triggered control (AIEC) with discontinuous characteristics is designed based on periodic sampling, where triggering instants are determined by the intermittent control (IC). Secondly, multiple pattern attack are modeled, as they can interrupt different edges and change the network topology. In addition, multi-pattern attacks for each link are independent and their impact on the coupling topology is analyzed. Thirdly, under destroyed network topology, this paper designs aperiodic intermittent event-triggered pinning control (AIEPC) by combining pinning control (PC) with the AIEC. Meanwhile, based on PC, the isolated node and pinned nodes form a like-directed spanning tree with an asymmetrical coupling matrix, where rooted at the isolated node and only directed connections between the isolated node and pinned nodes. Fourthly, using the segmentation analysis method and the inequality iteration technique, a sufficient condition for exponential synchronization of error system is obtained by considering the instants neighboring different intermittent control and attack intervals. Finally, a simulation example on Chua’s circuit network is provided to verify the validity of the theoretical results achieved in this paper.

Counter-rotating synchronization theory and experiment of tri-rotor actuated with dual-frequency considering adaptive global sliding mode control strategy

In petroleum drilling engineering, self-synchronous vibration screen with single-frequency actuation is difficult to implement the scheduled synchronous behavior caused by its invariance and instability of dynamic characteristics, which usually leads to reduction of the production efficiency. Hence, to solve the problem mentioned above, a dual-frequency counter-rotating synchronization control method among three exciters is presented by combining adjacent cross-coupling control (ACCC) structure with global sliding mode control (GSMC) theory. Firstly, motion differential equation of the vibration system in each direction is derived according to mathematical model of the tri-rotor vibration machine. Secondly, considering exponential reaching law and adaptive control algorithm, the adjacent cross-coupling controller and the vector controller of each induction motor are investigated to achieve the stable zero phase difference synchronization between double-frequency rotors. Subsequently, Runge-Kutta method is introduced to establish the electromechanical coupling control model and prove validity of the control theory. Meanwhile, it is also discussed that the rotors cannot obtain an ideal self-synchronization state since velocity of high-frequency motor is not strictly equal to twice that of low-frequency motor. Finally, based on the experimental test scheme, an experimental prototype related to controlled multi-rotor synchronization vibration system is designed independently, which further verifies the validity of theory and computer simulation. Research shows that the desirable synchronous state of the vibration system can be accurately controlled via the designed control strategy, and the control system can implement diversity of the dynamical characteristics, due to the existence of strong robustness.

Synchronization and stability of a vibrating system with two rigid frames driven by two groups of coaxial rotating exciters

This article explores the synchronization, stability and motion characteristics of the generalized dynamical model with two rigid frames (RFs) driven by two groups (even number) of coaxial rotating exciters. In light of this system’s generalized coordinates, we use Lagrange’s equations to derive the generalized differential equation of motion. The responses of absolute and relative motion of the generalized system are obtained using the transfer function method. The synchronization and stability criteria of multiple exciters are derived using the average method and Hamilton’s theory, respectively. Taking a dynamical model driven by two pairs of exciters as an example, the localized studies of generalized results are carried out. The stable synchronous solutions for phase differences and excitation frequency, the stability ability coefficient curves and the response curves are graphically presented considering the effect of two crucial dimensionless parameters on the stable synchronous states. The simulation results of the specific system are obtained using the fourth-order Runge-Kutta algorithms and compared with the numerical qualitative analysis results to reveal the high consistency between them and clarify the used methods’ effectiveness. The strength of this work stems from its use in the field of high power and large scale self-synchronization vibrating machines.

(Invited) Bio-Inspired Time Varying Networks for Novel Computing Primitives

As a result of a hundred million years of evolution, living animals have adapted extremely well to their ecological niche. Such adaptation implies species-specific interactions with their immediate environment by processing sensory cues and responding with appropriate behavior. Understanding how living creatures perform pattern recognition and cognitive tasks is of particular importance for computing architectures: by studying these information pathways refined over eons of evolution, researchers may be able to streamline the process of developing more highly advanced, energy efficient autonomous systems.With the advent of novel electronic and ionic components along with a deeper understanding of information pathways in living species, a plethora of opportunities to develop completely novel information processing avenues are within reach.Basal biological principles are highlighted, including phylogenies, ontogenesis, and homeostasis, with particular emphasis on network topology and dynamics. While in machine learning, system training is performed on virgin networks without any a priori knowledge, the approach proposed here distinguishes itself unambiguously by employing growth mechanisms as a guideline to design novel computing architectures. Within this framework, experiments on low-frequency relaxation type oscillators coupled via complex time-varying networks will be presents. The spatio-temporal development of the network results from a mutual interaction between the oscillator ensemble and the network structure. The blooming and pruning of suddenly appearing conductive bridges and their relation to the synchrony state of the oscillator ensemble will be discussed.

The swing of synchronization mediated by chimera states in fractional-order coupled Stuart-Landau oscillators

In this letter, we investigate the various dynamical behaviors in fractional-order coupled Stuart-Landau oscillator networks with the nonisochronicity parameter. We find that the nonisochronicity parameter can induce the swing of synchronization mediated by the imperfect synchronized state and the amplitude cluster state, and we verify the accuracy of the emergence of the swing of synchronization by the strength of incoherence and stability theory. Moreover, we discuss the effects of different parameters on the swing of synchronization mediated by the chimera state. First, as the nonisochronicity parameter increases, the range of the swing increases. Second, the decreasing of fractional-order derivative will lead to the reduction in the range of swing intervals. Third, the system exhibits the swing of synchronization mediated by the imperfect synchronized state when different initial conditions are employed. In particular, the system can show the imperfect breathing chimera state under symmetric initial conditions.

Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

ViewR: Architectural-Scale Multi-User Mixed Reality With Mobile Head-Mounted Displays.

The emergence of mobile head-mounted displays with robust "inside-out" markerless tracking and video-passthrough permits the creation of novel mixed reality (MR) experiences in which architectural spaces of arbitrary size can be transformed into immersive multi-user visualisation arenas. Here we outline ViewR, an open-source framework for rapidly constructing and deploying architectural-scale multi-user MR experiences. ViewR includes tools for rapid alignment of real and virtual worlds, tracking loss detection and recovery, user trajectory visualisation and world state synchronisation between users with persistence across sessions. ViewR also provides control over the blending of the real and the virtual, specification of site-specific blending zones, and video-passthrough avatars, allowing users to see and interact with one another directly. Using ViewR, we explore the transformation of large architectural structures into immersive arenas by creating a range of experiences in various locations, with a particular focus on architectural affordances such as mezzanines, stairs, gangways and elevators. Our tests reveal that ViewR allows for experiences that would not be possible with pure virtual reality, and indicate that, with certain strategies for recovering from tracking errors, it is possible to construct large scale multi-user MR experiences using contemporary consumer virtual reality head-mounted displays.

The effectiveness of group interpersonal synchrony in young autistic adults' work environment: A mixed methods RCT study protocol.

Few autistic adults are able to integrate successfully into the world of work given their difficulties adapting to the social and stressful aspects of work environments. Interpersonal synchrony, when two or more individuals share body movements or sensations, is a powerful force that consolidates human groups while promoting the ability to self-regulate and cooperate with others. The abilities to self-regulate and cooperate are crucial for maintaining a calm and productive work environment. This study protocol outlines research that aims to assess the effects of group interpersonal synchrony on prosociality and work-related stress of young autistic adults in their work environment. This mixed-methods randomized controlled trial will investigate two movement-based group synchronous and non-synchronous intervention conditions. The sample will be composed of young adults enrolled in an innovative Israeli program designed to integrate cognitively-abled 18- to 25-year-old autistic adults into the Israeli army work force. The movement-based intervention sessions will take place in groups of 10-14 participants, once a week for 10 weeks. Questionnaires, behavioral collaborative tasks and semi-structured interviews will be conducted. Quantitative data will be collected for each participant at three points of time: before and after the intervention period, and 17 weeks after the end of the intervention. Qualitative data will be collected after the intervention period in interviews with the participants. Little is known about interventions that promote successful integration into social and stressful work environments. The findings are likely to shed new light on the use of group interpersonal synchrony in autistic individuals at work. NCT05846308.

Synchronization of Kuramoto-oscillator networks under event-triggered impulsive control with noise perturbation

This paper studies the stochastic average synchronization of Kuramoto-oscillator networks under event-triggered impulsive control (ETIC) strategies, in which the event-triggered mechanism (ETM) determines the impulsive control time sequence. The continuous ETM is designed to avoid the Zeno behavior by continuous measuring, and the periodic ETM is proposed by periodic sampling. Based on the proposed ETIC methods, several sufficient conditions for the stochastic average synchronization of Kuramoto-oscillator networks are established. Unlike time-triggered impulsive control, where the triggered instants are pre-designed, ETIC is activated only upon the occurrence of an event, so synchronization conditions are heavily dependent on the ETM. Furthermore, there is no control input between two successive triggering instants, and the control input is required only at the trigger instants. Finally, numerical simulations are shown to illustrate the effectiveness of the theoretical results. Besides, it is found that the presence of noise may favor the synchronization of Kuramoto-oscillator networks.

Cloud‐mediated self‐triggered synchronisation of a general linear multi‐agent system over a directed graph

AbstractThe authors propose a self‐triggered synchronisation control method of a general high‐order linear time‐invariant multi‐agent system through a cloud repository. In the cloud‐mediated self‐triggered control, each agent asynchronously accesses the cloud repository to obtain past information about its neighbouring agents. Then, the agent predicts future behaviours of its neighbours as well as of its own and locally determines its next access time to the cloud repository. In the case of a general high‐order linear agent dynamics, each agent has to estimate exponential evolution of its trajectory characterised by eigenvalues of a system matrix, which is different from single/double integrator or first‐order linear agents. The authors’ proposed method deals with exponential behaviours of the agents by tightly evaluating the bounds on matrix exponentials. Based on these bounds, the authors design the self‐triggered controller through a cloud that achieves the bounded state synchronization of the closed‐loop system without exhibiting any Zeno behaviours. The effectiveness of the proposed method is demonstrated through the numerical simulation.