Synchronous State Research Articles

Synchronization of networked mechanical systems without velocity information

AbstractThis paper studies the synchronization problem in a network of interconnected mechanical systems where the velocity information of the interacting agents is unavailable. To achieve this, a distributed law related to the kinetic and potential energies of the considered system is proposed. Specifically, by introducing an auxiliary system and a distributed filter, it is shown that the proposed algorithm enables the synchronization of the considered system by merely using the local position measurements. Moreover, it is also shown that, compared with the existing literature, the derived synchronization conditions are irrelevant to the eigenvalues of Laplacian matrix, thus circumventing the global information of the underlying system. Moreover, on condition that the absolute position information is available, it is also shown that apart from the synchronization of agents, the discrepancy between the position variable of the original system and that of the auxiliary variable tends to zero eventually. Finally, a concrete example and some comparisons are conducted to support the formulated setup and the obtained theoretical results.

Periodic systems have new classes of synchronization stability

The master stability function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the master stability function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability. Published by the American Physical Society 2024

Synchronization characteristics and stable states of four co-rotating vibrators with balanced slanted elliptical trajectory

In the petroleum drilling and mining screening industries, our goal is to enhance excitation force, integrate circular screening with rectilinear transport to obtain the balanced slanted elliptical trajectory (BSET), and reduce screen mesh clogging. This work investigates the synchronization characteristics and stable states of four co-rotating vibrators. The novelty of this work lies in using a novel vibration model to achieve the BSET in the synchronization state and in further considering the influence of a new skewing angle between two eccentric rotors (ERs), which are few in previous vibration screening field. Initially, the vibration model is extracted from the designed prototype. Then, in accordance with Routh–Hurwitz criterion, the synchronization and stability are theoretically analyzed using small parameters of vibrator velocity and phase differences (PDs). The synchronization characteristics related to mechanical structures are discussed via numerical calculation and experimental verification. Results reveal that the synchronization implementation is adversely affected by the skewing angle, even leading to unordered behaviors. Achieving zero-phase or in-phase synchronization with four vibrators is only feasible with a larger symmetric distance and installation angle. This work can contribute a foundation for designing some new types of large vibration screening and material conveyance machines.

A continuous-discrete adaptive observer with a diagonal gain matrix and sigma-modification: applications in chaos synchronization and dynamical state estimation

In this paper, we propose an improved continuous-discrete observer with enhanced convergence properties and reduced sensitivity to persistent excitations. Our approach introduces several key innovations, including a customised diagonal gain matrix which improves the convergence speed, a sigma-modification technique that relaxes the persistent excitation conditions, and a weighting factor tailored to optimise the estimation of unknown parameters. Through comprehensive numerical experiments, we illustrate the effectiveness of our observer in two distinct scenarios. Firstly, we demonstrate its application in synchronising a 4-component chaotic dynamical system. Secondly, we showcase its utility in tracking a reduced 2-component chemical engineering process. Our simulation results reveal that the proposed observer outperforms existing methods by achieving quicker convergence and higher estimation accuracy. This study contributes to the advancement of adaptive observer design, offering valuable insights for its application across diverse fields.

Collective swimming pattern and synchronization of fish pairs (Gobiocypris rarus) in response to flow with different velocities.

Collective behaviors in moving fish originate from social interactions, which are thought to be driven by beneficial factors, such as predator avoidance and reduced energy expenditure. Despite numerical simulations and physical experiments aiming at the hydrodynamic mechanisms and interaction rules, how shoaling is influenced by flow velocity and group size is still only partially understood. In this study, spatial distributions, kinematics, and synchronization states between pairs (smallest subsystem of a shoal) of Gobiocypris rarus were investigated in a recirculating swim tunnel with increasing flow velocities from 0.1 to 0.5 m/s (Ucrit = 0.6 m/s). Tests of single fish were also conducted as the control group. The results of spatial distributions showed that fish pairs preferred to swim in the side-by-side configuration under high flows, while under low flows the neighboring fish's positions were more uniformly distributed around the focal fish in the transverse direction. Kinematic analysis revealed that fish pairs adopted similar tail beats (i.e., frequency and Strouhal number) as single fish in low flows, while in high flows both the frequency and Strouhal number of fish pairs were slightly lower. Moreover, the synchronization rates of fish pairs were found to increase with flow velocities, suggesting that synchronized swimming may be beneficial, especially in high flows.

Drifts of the substellar points of the TRAPPIST-1 planets

Accurate modeling of tidal interactions is crucial for interpreting recent JWST observations of the thermal emissions of TRAPPIST-1 b and c and for characterizing the surface conditions and potential habitability of the other planets in the system. Indeed, the rotation state of the planets, driven by tidal forces, significantly influences the heat redistribution regime. Due to their proximity to their host star and the estimated age of the system, the TRAPPIST-1 planets are commonly assumed to be in a synchronization state. In this work, we present the recent implementation of the co-planar tidal torque and forces equations within the formalism of Kaula in the N-body code Posidonius. This enables us to explore the hypothesis of synchronization using a tidal model well suited to rocky planets. We studied the rotational state of each planet by taking into account their multi-layer internal structure computed with the code Burnman. Our simulations show that the TRAPPIST-1 planets are not perfectly synchronized but oscillate around the synchronization state. Planet-planet interactions lead to strong variations on the mean motion and tides fail to keep the spin synchronized with respect to the mean motion. As a result, the substellar point of each planet experiences short oscillations and long-timescale drifts that lead the planets to achieve a synodic day with periods varying from $55$ years to $290$ years depending on the planet.

The Chaotic Behavior of an Optical Artificial Neuron

ABSTRACT The operation of an optical neural network via a feed-forward (FF) configuration is experimentally simulated in the laboratory. The FF setup is tested using optical injection (OI), and the behavior of follower laser diodes (FLDs) subjected to chaotic modulation is examined. The last two laser diodes (LDs) are exposed to different weights of chaotic modulated signals through optical filtration and attenuation. Observations of the emissions from these two FLDs during FF operation are verified by frequency spectra calculated from time-series data. Signal broadening is assessed by measuring the full width at half maximum (FWHM), and chaotic signal spikes are analyzed by counting the number of peaks associated with signal amplitudes for the FLDs. Additionally, LD control parameters, including the bias voltage of the influencer laser diodes (ILD1, ILD2) and two additional FLDs, are examined. A maximum FWHM of 1.25 GHz for FLD2 is observed with a bias voltage of 3.6 V and a modulated signal attenuation of −12 dB. To determine the synchronization state, the correlation between the ILDs and FLDs is calculated. Results indicate fluctuations between negative and positive values, with the best correlation value being 0.4. These results confirm anti-synchronized ILD-FLDs, which are crucial for ensuring privacy in transmitting units within a chaotic optical communication system simulating an optical neural network.

Achieving synchronization and chimera state of modular neural networks by using dynamic learning to adjust electromagnetic induction

Achieving synchronization and chimera state of modular neural networks by using dynamic learning to adjust electromagnetic induction

Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system

In oil drilling processes, vibrating screen is a crucial solid control equipment for separating harmful solid-phase particles. However, the conventional utilization of either dual-motor or triple-motor is inadequate demanding the excitation force of large vibrating equipment. Moreover, self-synchronization in zero phase is difficult to achieve in multiple motors system. To avoid cancellation of the excitation force caused by the phase inconsistency of multiple motors, the adoption of a four-motor excitation with torsion spring coupling system is proposed this work. Initially, the mathematical model of the vibrating system is formulated through the Lagrange's equation. Subsequently, the steady-state solution is determined using Laplace transform. Then the conditions and characteristics in stable equilibrium state are elucidated employing the small parameter averaging method. Ultimately, the reliability and applicability of the theoretical results are substantiated through numerical simulations. The findings reveal that with the increase of the torsion spring stiffness, the phase difference between the motors connected by torsion springs (MCTSs) is exponentially decreased, and desired zero-phase synchronization in engineering is eventually achieved. Furthermore, the present study uncovers two distinct synchronization mechanisms in the torsion spring coupling system: mechanical controlled synchronization between MCTSs is inevitably achieved, while the self-synchronization between motors unconnected by torsion springs (MUTSs) is limited by the synchronization conditions. The study provides valuable insights for designing mechanical controlled synchronization and self-synchronization vibrating machines.

Synchronization of nonlinear neural networks with hybrid couplings and uncertain time-varying perturbations: A novel distributed-delay impulsive comparison principle

This paper investigates the synchronization of nonlinear drive-response neural networks subject to uncertain time-varying perturbations, non-delayed coupling, and distributed delay coupling. To address the influence of distributed and discrete delays on the system, we establish a novel impulsive comparison principle, extending the Halanay inequality. By leveraging Lyapunov stability theory, we derive sufficient conditions for the exponential synchronization of the neural networks using a delayed impulsive controller with historical status information. This approach relaxes the conventional constraint that impulsive delays must be smaller than impulsive intervals, thereby generalizing existing synchronization results for distributed delay networks. Numerical simulations for chaotic neural networks validate the theoretical results and demonstrate the sensitivity of the control gain matrix.

Synchronization of Delayed Memristor-Based Neural Networks via Pinning Control With Local Information.

In this article, a novel pinning control method, only requiring information from partial nodes, is developed to synchronize drive-response memristor-based neural networks (MNNs) with time delay. An improved mathematical model of MNNs is established to describe the dynamic behaviors of MNNs accurately. In the existing literature, pinning controllers for synchronization of drive-response systems were designed based on information of all nodes, but in some specific situations, the control gains may be very large and challenging to realize in practice. To overcome this problem, a novel pinning control policy is developed to achieve synchronization of delayed MNNs, which depends only on local information of MNNs, for reducing communication and calculation burdens. Furthermore, sufficient conditions for synchronization of delayed MNNs are provided. Finally, numerical simulation and comparative experiments are conducted to verify the effectiveness and superiority of the proposed pinning control method.

Asymptotic Synchronization for Caputo Fractional-Order Time-Delayed Cellar Neural Networks with Multiple Fuzzy Operators and Partial Uncertainties via Mixed Impulsive Feedback Control

To construct Caputo fractional-order time-delayed cellar neural networks (FOTDCNNs) that characterize real environments, this article introduces partial uncertainties, fuzzy operators, and nonlinear activation functions into the network models. Specifically, both the fuzzy AND operator and the fuzzy OR operator are contemplated in the master–slave systems. In response to the properties of the considered cellar neural networks (NNs), this article designs a new class of mixed control protocols that utilize both the error feedback information of systems and the sampling information of impulse moments to achieve network synchronization tasks. This approach overcomes the interference of time delays and uncertainties on network stability. By integrating the fractional-order comparison principle, fractional-order stability theory, and hybrid control schemes, readily verifiable asymptotic synchronization conditions for the studied fuzzy cellar NNs are established, and the range of system parameters is determined. Unlike previous results, the impulse gain spectrum considered in this study is no longer confined to a local interval (−2,0) and can be extended to almost the entire real number domain. This spectrum extension relaxes the synchronization conditions, ensuring a broader applicability of the proposed control schemes.

Microstate D as a Biomarker in Schizophrenia: Insights from Brain State Transitions.

Objectives. There is a significant correlation between EEG microstate and the neurophysiological basis of mental illness, brain state, and cognitive function. Given that the unclear relationship between network dynamics and different microstates, this paper utilized microstate, brain network, and control theories to understand the microstate characteristics of short-term memory task, aiming to mechanistically explain the most influential microstates and brain regions driving the abnormal changes in brain state transitions in patients with schizophrenia. Methods. We identified each microstate and analyzed the microstate abnormalities in schizophrenia patients during short-term memory tasks. Subsequently, the network dynamics underlying the primary microstates were studied to reveal the relationships between network dynamics and microstates. Finally, using control theory, we confirmed that the abnormal changes in brain state transitions in schizophrenia patients are driven by specific microstates and brain regions. Results. The frontal-occipital lobes activity of microstate D decreased significantly, but the left frontal lobe of microstate B increased significantly in schizophrenia, when the brain was moving toward the easy-to-reach states. However, the frontal-occipital lobes activity of microstate D decreased significantly in schizophrenia, when the brain was moving toward the hard-to-reach states. Microstate D showed that the right-frontal activity had a higher priority than the left-frontal, but microstate B showed that the left-frontal priority decreased significantly in schizophrenia, when changes occur in the synchronization state of the brain. Conclusions. In conclusion, microstate D may be a biomarker candidate of brain abnormal activity during the states transitions in schizophrenia, and microstate B may represent a compensatory mechanism that maintains brain function and exchanges information with other brain regions. Microstate and brain network provide complementary perspectives on the neurodynamics, offering potential insights into brain function in health and disease.

Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane

The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.

Synchronization on complex dynamical networks via intermittently sampled-data pinning control

Each specific control strategy has a unique advantage, and combining multiple control strategies can harness the advantages of these strategies. Designing new control strategies by integrating different control strategies is an interesting and challenging topic. This paper introduces an intermittently sampled-data pinning (ISP) control strategy, which merges intermittent control, sampled-data control and pinning control, to study synchronization on complex dynamical networks. The ISP control strategy is proposed to solve three difficulties: first, the controllers transmitting feedback signals may be discontinuous; second, the controllers often cannot operate continuously in practical applications; third, it is usually hard to control all nodes in a dynamical network as the network size is huge. Sufficient conditions are obtained for realizing synchronization on dynamical networks. Furthermore, time delays are incorporated into the proposed control strategy to address the untimely reception of feedback signals and achieve the synchronization conditions on dynamical networks. Finally, two numerical examples demonstrate the effectiveness of the proposed control method.

Coexistence of multistable synchronous states in a three-oscillator system with higher-order interaction.

We study a three-oscillator system with pairwise (1-simplex) and triadic (2-simplex) interactions, and focus on how the interplay between these two types of interactions influences synchronous dynamics. Using a minimal model, dynamical phenomena in systems that have been previously studied under the thermodynamic limit (N→∞) are further clarified. Various synchronous states, including in-phase and antiphase synchronous states, as well as partial synchronous states are demonstrated. Meanwhile, significant multistable behaviors are revealed. Our work extends previous research on pairwise and triadic interactions, which can deepen our understanding of the impact of correlation between higher-order interaction and multistability. These dynamic phenomena bear resemblance to the diverse synchronization patterns of the heart, and they also serve as pivotal factors in information storage and memory retention within the brain.

Deep reinforcement learning using deep-Q-network for Global Maximum Power Point tracking: Design and experiments in real photovoltaic systems

This paper presents a methodology for integrating Deep Reinforcement Learning (DRL) using a Deep-Q-Network (DQN) agent into real-time experiments to achieve the Global Maximum Power Point (GMPP) of Photovoltaic (PV) systems under various environmental conditions. Conventional methods, such as the Perturb and Observe (P&O) algorithm, often become stuck at the Local Maximum Power Point (LMPP) and fail to reach the GMPP under Partial Shading Conditions (PSC). The main contribution of this work is the experimental validation of the DQN agent's implementation in a synchronous DC-DC Buck converter (step-down converter) un-der both uniform and PSC conditions. Additionally, we establish a testing pipeline for DRL models. The DQN agent's performance is evaluated alongside the P&O algorithm. Results consistently indicate the DQN agent's superiority over the P&O algorithm in all simulated scenarios. Although this trend does not entirely replicate in real-world test setups, significant results are observed. Specifically, in PSC sce-narios where the P&O algorithm becomes trapped at an LMPP, the DQN algorithm extracts up to 63.5 % more power than the P&O algorithm. An open repository is available, containing PCB schematic designs and layouts, along with the code used for model training and deployment.

Intermittent dynamic event-triggered control for synchronization of Takagi–Sugeno fuzzy competitive neural networks with leakage delay and different time scales

Because competitive neural networks (CNNs) can simulate the phenomena of lateral inhibition among neurons, their dynamics are attracting increasing attention, which motives us to investigate the global exponential synchronization issue of multiple time-delays fuzzy CNNs (MDFCNNs) with different time scales in this article. Firstly, to solve the significant resource wastage problem caused by the time-triggered mechanism previously adopted in CNNs, a novel intermittent dynamic event-triggered mechanism is proposed. It is worth mentioning that the fuzzy logic systems are also utilized in this model and controller, effectively handling the uncertainties and nonlinearities in practical problems. Secondly, by designing the intermittent static/dynamic event-triggered mechanism, we derive the global exponential synchronization conditions for MDFCNNs with different time scales under a simpler and more implementable controller composed of a linear negative feedback control term. We also utilize the reduction to absurdity to demonstrate the nonexistence of Zeno behavior for the error system of master-slave CNNs. Furthermore, we provide several corollaries to further indicate the generality of the model and the cost savings of the control mechanism. Finally, we provide an example and some comparisons to demonstrate the efficiency of the derived theoretical findings.

Sense of embodiment with synchronized avatar during walking in mixed reality.

Gait guidance systems that synchronize the gait rhythm with an avatar in a mixed reality (MR) environment are attracting attention owing to their rehabilitation applications. More effective gait guidance can be achieved by changing body sensations for the sense of embodiment (SoE), which refers to the feeling of owning, controlling, and being inside a body in MR. This study investigated full-body synchronous motion between a human and a virtual avatar to enhance the SoE in walking with actual position changes in the real world. The full-body motion and gait rhythm were measured using body-worn inertial measurement units and a visual avatar was provided through a transparent head-mounted display. The results showed that the SoE of the participants was enhanced under higher synchronization conditions. In addition, questionnaire results showed that the SoE in the synchronous condition was significantly higher than that in the asynchronous condition, and the SoE in the self-avatar condition was significantly higher than that in the other-avatar condition. This indicates that a higher synchronization level with the appearance of an avatar leads to a stronger SoE in the human perception mechanism, which is important for potential application in medical or other fields.

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.