Property Of Synchronization Research Articles

Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors

The investigation of collective behaviors and synergies in coupled systems holds great significance in many fields. In this paper, we propose the coupled system of overdamped fluctuating–damping oscillators in a general network framework. Our initial theoretical analysis focuses on the system’s synchronization and stability, revealing that both the first and second moments of the mean field are asymptotic stability, and the system exhibits a property of stochastic asymptotic synchronization with the mean field, irrespective of coupled structures. Furthermore, we explore the system’s collective behaviors by analyzing the output amplitude amplification (OAA), where we observe the emergence of generalized stochastic resonance (GSR) phenomena. Finally, we numerically verify the influence of system parameters on stability and synchronization in different coupled structures by introducing the mean first stability time and mean first synchronization time in the simulations. Our findings indicate that the structure does not significantly influence the system stability, whereas it does play a synergistic role in influencing the synchronization. Moreover, we further extend the investigation in complex networks, and observe the non-monotonous phenomena of mean first synchronization time varying with the heterogeneity.

Strongly Synchronized Redactable Blockchain Based on Verifiable Delay Functions

As one of the crucial features of the blockchain technique, immutability plays the most important role in winning the so-called praise of the "trust machine" for blockchain. However, there are two sides to everything. The property of immutability of blockchain is applied maliciously sometimes, say publishing harmful or even dangerous data and hindering authorities’ law enforcement. To address this issue, authorized redactability of blockchain was introduced to support block modification without lowering the fundamental basis of security and trust that is cherished on the blockchain. During the past years, several techniques of redactable blockchain were proposed, mainly based on the well-known chameleon hashing. Different from existing methodologies, we propose a new redactable blockchain scheme for permissioned settings in this paper. We first employ the trapdoor verifiable delay function to attach a time-lapse proof to each block. Moreover, the trapdoor is used to quickly construct a chain fork to redact blocks that are authorized to alter. Our proposal does not need to rollback irrelevant blocks. As a remarkable and unique feature, our proposal realizes the property of strong synchronization of redaction, which means that all nodes in the blockchain will have identical views on the chain even after some blocks are altered. Security analysis shows that the consistency of the chain is guaranteed, and the long-range attack can be resisted effectively. The performance comparison shows that our method is feasible and practical.

Mesh-Free Interpolant Observables for Continuous Data Assimilation

This paper considers a nudging-based scheme for data assimilation for the two-dimensional (2D) Navier-Stokes equations (NSE) with periodic boundary conditions and studies the synchronization of the signal produced by this algorithm with the true signal, to which the observations correspond, in all higher-order Sobolev topologies. This work complements previous results in the literature where conditions were identified under which synchronization is guaranteed either with respect to only the $H^1$--topology, in the case of general observables, or to the analytic Gevrey topology, in the case of spectral observables. To accommodate the property of synchronization in the stronger topologies, the framework of general interpolant observable operators, originally introduced by Azouani, Olson, and Titi, is expanded to a far richer class of operators. A significant effort is dedicated to the development of this more expanded framework, specifically, their basic approximation properties, the identification of subclasses of such operators relevant to obtaining synchronization, as well as the detailed relation between the structure of these operators and the system regarding the syncrhonization property. One of the main features of this framework is its "mesh-free" aspect, which allows the observational data itself to dictate the subdivision of the domain. Lastly, estimates for the radius of the absorbing ball of the 2D NSE in all higher-order Sobolev norms are obtained, thus properly generalizing previously known bounds; such estimates are required for establishing the synchronization property of the algorithm in the higher-order topologies.

Knowledge-driven feature component interpretable network for motor imagery classification

Objective. The end-to-end convolutional neural network (CNN) has achieved great success in motor imagery (MI) classification without a manual feature design. However, all the existing deep network solutions are purely datadriven and lack interpretability, which makes it impossible to discover insightful knowledge from the learned features, not to mention to design specific network structures. The heavy computational cost of CNN also makes it challenging for real-time application along with high classification performance. Approach. To address these problems, a novel knowledge-driven feature component interpretable network (KFCNet) is proposed, which combines spatial and temporal convolution in analogy to independent component analysis and a power spectrum pipeline. Prior frequency band knowledge of sensory-motor rhythms has been formulated as band-pass linear-phase digital finite impulse response filters to initialize the temporal convolution kernels to enable the knowledge-driven mechanism. To avoid signal distortion and achieve a linear phase and unimodality of filters, a symmetry loss is proposed, which is used in combination with the cross-entropy classification loss for training. Besides the general prior knowledge, subject-specific time-frequency property of event-related desynchronization and synchronization has been employed to construct and initialize the network with significantly fewer parameters. Main results. Comparison of experiments on two public datasets has been performed. Interpretable feature components could be observed in the trained model. The physically meaningful observation could efficiently assist the design of the network structure. Excellent classification performance on MI has been obtained. Significance. The performance of KFCNet is comparable to the state-of-the-art methods but with much fewer parameters and makes real-time applications possible.

Robust distributed synchronization of networked linear systems with intermittent information

The problem of synchronization of multiple linear time-invariant systems connected over a network with asynchronous and intermittently available communication events is studied. To solve this problem, we propose a controller with hybrid dynamics, namely, the controller utilizes information transmitted to it during discrete communication events and exhibits continuous dynamics between such events. Due to the additional continuous and discrete dynamics inherent to the interconnected networked systems and communication structure, we use a hybrid systems framework to model and analyze the closed-loop system. The problem of synchronization is then recast as a set stabilization problem and, by employing Lyapunov stability tools for hybrid systems, sufficient conditions for asymptotic stability of the synchronization set are provided. Furthermore, we show that the property of synchronization is robust to perturbations. Numerical examples illustrating the main results are included.

Disturbance attenuation of complex dynamical systems through interaction topology design

Control of complex systems has been extensively investigated over the past decades. Most of the investigations concern the collective dynamical property of synchronization, while the issue of disturbance attenuation of complex systems is not widely considered. This is particularly true for the problem of simultaneous disturbance attenuation for all agents with (all) non-identical nodes dynamics. Methodologically, for both synchronization and disturbance attenuation, approaches can be taken by either feedback compensation, or properly designed switching signals. The concept of disturbance attenuation through topology design has not been recognized. This note aims to develop this idea. Straightforward yet interesting results are obtained. Numerical examples are illustrated to verify the claims while related design issues are also discussed.

Synchronization of strange non-chaotic attractors via unidirectional coupling of quasiperiodically-forced systems

In this paper, we present a numerical investigation on the robust synchronization phenomenon observed in a unidirectionally-coupled quasiperiodically-forced simple nonlinear electronic circuit system exhibiting strange non-chaotic attractors (SNAs) in its dynamics. The SNA obtained in the simple quasiperiodic system is characterized for its SNA behavior. Then, we studied the nature of the synchronized state in unidirectionally coupled SNAs by using the Master-Slave approach. The stability of the synchronized state is studied through the master stability functions (MSF) obtained for coupling different state variables of the drive and response system. The property of robust synchronization is analyzed for one type of coupling of the state variables through phase portraits, conditional lyapunov exponents and the Kaplan-Yorke dimension. The phenomenon of complete synchronization of SNAs via a unidirectional coupling scheme is reported for the first time.

Finite-size scaling in globally coupled phase oscillators with a general coupling scheme

We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize fluctuations in coupled oscillator systems of large but finite size and understand a universal property of synchronization. These exponents have been identified for the sinusoidal coupling but not fully studied for other coupling schemes. Herein, for a general coupling function including a negative second harmonic term in addition to the sinusoidal term, we numerically estimate the critical exponent of the correlation size, denoted by $\nu_+$, in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of $\nu_+$ is approximately 5/2 for the sinusoidal coupling case, which is consistent with the well-known theoretical result. Second, we show that the value of $\nu_+$ increases with an increase in the strength of the second harmonic term. Our result implies that the critical exponent characterizing synchronization transition largely depends on the coupling function.

A New Hardware-oriented Spiking Neuron Model Based on SET and Its Properties

In this paper, a new simple hardware-oriented spiking neuron model is proposed. It is mainly based on one of intrinsic features of single- electron transistor (SET)––Coulomb Oscillation. In fact, Coulomb Oscillation can be considered as current pulses under the gate's voltage, which is similar with the pulses of spiking neurons. Accordingly, the circuit structure of spiking neuron model has been designed. By simulation on the PSPICE, the proposed new model can show different spiking types according to the different input signals and implement information encoding. The model can exhibit the property of synchronization. Unlike traditional neuron model, the proposed new model has the capacity of integrating both spatial and temporal signals. In addition the phase encoding is also involved. So the experiments’ results demonstrate that the model is an implement way of hardware-oriented spiking neuron models or even spiking neural networks (SNN).

BINARY CHAOS SYNCHRONIZATION IN ELEMENTARY CELLULAR AUTOMATA

It is shown that 8 of all 256 elementary cellular automata have the property of chaos synchronization using a binary driving sequence. The binary synchronization signal ensures good noise robustness. A simple measure for characterizing long periodic cycles as being "chaotic" was introduced. It is also shown that certain relations between the profile of attractors shaped by the local rule in the finite state space and the property of chaos synchronization exists. A simple modulation–demodulation scheme is proposed allowing to build spread spectrum communication links at low implementation costs while the cellular automata state space (number of cells) can be taken as large as required by cryptographic reasons.

Renewal aging as emerging property of phase synchronization

We propose a dynamical model generating the same non-Poisson renewal events as those currently found in complex systems as the blinking quantum dots and the human brain. Our results suggest that these complex systems can be interpreted as a set of synchronized neurons.

Convergence Property of Noise-induced Synchronization

Convergence Property of Noise-induced Synchronization

Study on the measure synchronization in coupled Hamiltonian systems*

The phenomenon of measure synchronization is an important property in coupl ed Hamiltonian systems. In this paper, we investigate the measure synchronizati on in a chaotic system, and the regularity of phase difference is also discusse d in the regular coupled systems and the chaotic coupled system.A new method is proposed for determining the critical coupled strength of transition to the mea sure synchronization. At the same time, we have studied the influence of Gaussi an white noise on the measure synchronization. It is significant to investigate the conservative system using the property of measure synchronization.

Generation of 1/f noise in locked systems working in nonlinear mode

Properties of the phase fluctuations of a nonlinear oscillator were investigated. The multiscale aspect of synchronization is experimentally confirmed with the observation of lockings at any rational ratio. This global property of synchronization is associated with a local one by the study of the phase locked loop (PLL) under nonlinear conditions. We show that the discontinuity between the locking and the free-run state is characterized by the presence of slow temporal variations that induce a low frequency spectrum. An experimental verification of the increase of fluctuations confirms the classical results, which associate 1/f noise to nonlinearity, autosimilarity and regularity, represented here by the synchronization.

Optical chaotic AM demodulation by asymptotic synchronization

Synchronization between two identical chaotic systems (drive and response) with different initial conditions can be achieved provided that the conditional Lyapunov exponents are all negative. Adding an AM signal to the drive system, the two systems become asymptotically synchronized. The AM signal can be recovered by utilizing the property of the asymptotic synchronization. Chaotic AM noise is present as a direct result of the chaotic AM demodulation. Signal-to-chaotic-AM-noise ratio is calculated as a function of the signal amplitude.