搜索结果：synchronization

In this paper, we introduce the synchronization zeta function associated with a pair of self-maps of a topological space and investigate its properties. We also define the growth rate of synchronization points and derive an explicit formula in the setting of endomorphisms of compact, connected Abelian groups. In addition, we establish Gauss congruences and describe the asymptotic behavior for the sequence of numbers of synchronization points, under the assumption that the synchronization zeta function is rational. Further, we discuss connections with topological entropy and Reidemeister torsion.

We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as the parent for the subsequent node. Our analysis focuses on two distinct synchronization behaviors: parent-child synchronization, defined by the vanishing distance between successive nodes along the chain, and sibling synchronization, corresponding to the convergence of the states of two child nodes. Our findings reveal significant differences in these two type of synchronization mechanisms, which are closely associated with the probability distribution of the state of parent node. Theoretical analysis and simulations with the logistic map support our findings. We further investigate numerical aspects of the implementation corresponding to cases for which the simulated regimes differ from the theoretically predicted one due to computational finite accuracy. We perform a detailed study on how instabilities are numerically suppressed or amplified along the chain. In some cases, a properly adjusted computational scheme can solve this problem.

We show how to utilize magnetostriction to synchronize two mechanical vibration modes in a cavity magnomechanical system. The dispersive magnetostrictive interaction provides necessary nonlinearity required for achieving synchronization. Strong phase correlation between two mechanical oscillators can be established, leading to the synchronization robust against thermal noise. We develop a theoretical framework to analyze the synchronization by solving the constraint conditions of steady-state limit cycles. We determine that the strong cavity-magnon linear coupling can enhance and regulate the synchronization, which offers a new path to modulate synchronization. The work reveals a new mechanism for achieving and modulating synchronization and indicates that cavity magnomechanical systems can be an ideal platform to explore rich synchronization phenomena.

Synchronization blockade refers to an interferometric cancellation of quantum synchronization. In this manuscript, we show how the choice of synchronization measure and Hamiltonian symmetries affect the discussion of synchronization blockade. Using counting principles, we prove a general theorem that synchronization blockade cannot be observed in an $N-$level system when the coherent state used to define the diagonal limit-cycle state is in the full $SU(N)$ group. We present several illustrative examples of synchronization blockade in multi-level systems and prove that information-theoretic measures of synchronization can also observe synchronization blockade-like behavior by an appropriate choice of the set of limit cycle states.

Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object identities, supporting complex datatypes, handling dependencies among them, and object-aware synchronization. Object-centric Petri nets with identifiers (OPIDs) partially address these needs but treat objects as unstructured identifiers (e.g., order and item IDs), overlooking the rich semantics of complex data values (e.g., item prices or other attributes). To overcome these limitations, we introduce data-aware OPIDs (DOPIDs), a framework that strictly extends OPIDs by incorporating structured data manipulation capabilities, and full synchronization mechanisms. In spite of the expressiveness of the model, we show that it can be made operational: Specifically, we define a novel conformance checking approach leveraging satisfiability modulo theories (SMT) to compute data-aware object-centric alignments.

We propose a novel and efficient, custom frame synchronization architecture aimed at rapid deployment on any hardware platform. Frame synchronization is the process of discerning valid data frames from an incoming transmission and in this article it is accomplished by attaching distinctive binary overhead sequences on the frame. These sequences act as markers for the frames and enable the capture of their payload. They have certain properties and can be detected by using only simple hardware constructs like XNOR gates and few-bit adders with adequate accuracy. A low-cost commercial FPGA was used for implementation (NEXYS 4 DDR).

Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e., synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry - henceforth the phenomenon of "synchronization within synchronization." Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological netw

The study of network synchronization has attracted increasing attention recently. In this paper, we strictly define a class of networks, namely effective networks, which are synchronizable and orientable networks. We can prove that all the effective networks with the same size have the same spectra, and are of the best synchronizability according to the master stability analysis. However, it is found that the synchronization time for different effective networks can be quite different. Further analysis show that the key ingredient affecting the synchronization time is the maximal depth of an effective network: the larger depth results in a longer synchronization time. The secondary factor is the number of links. The more links connecting the nodes in the same layer (horizontal links) will lead to longer synchronization time, while the increasing number of links connecting nodes in neighboring layers (vertical links) will accelerate the synchronization. Our findings provide insights into the roles of horizontal and vertical links in synchronizing process, and suggest that the spectral analysis is helpful yet insufficient for the understanding of network synchronization.

We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the quantum synchronization effects between optomechanical systems and find that the error between the systems and the fluctuation of error are sensitive to coupling intensity by calculating the largest Lyapunov exponent of the model and quantum fluctuation, respectively. Through taking the appropriate coupling intensity, we can control quantum synchronization even under different logical relationship between switches. Finally, we simulate the dynamical evolution of the system to verify the quantum synchronization criterion and to show the ability of synchronization control.

This article studies the interrelation between the determining modes property in the two-dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the reconstruction property of two filtering algorithms for continuous data assimilation applied to the 2D NSE. These two properties are realized as manifestations of a more general phenomenon of "self-synchronous intertwinement." It is shown that this concept is a logically stronger form of asymptotic enslavement, as characterized by the existence of finitely many determining modes in the 2D NSE. In particular, this stronger form is shown to imply convergence of the direct-replacement filter and the nudging filter from continuous data assimilation (CDA), and then subsequently invoked to show that convergence in these filters implies that the 2D NSE possesses finitely many determining modes. The main achievement of this article is to therefore to develop a new conceptual framework, that of self-synchronous intertwinement, through which the precise inter-relationship between the determining modes property and synchronization phenomenon in these CDA filters is rigorously established and made decisively clear. The theoreti

We report the nature of transitions from nonsynchronous to complete synchronization (CS) state in arrays of time-delay systems, where the systems are coupled with instantaneous diffusive coupling. We demonstrate that the transition to CS occurs distinctly for different coupling configurations. In particular, for unidirectional coupling, locally (microscopically) synchronization transition occurs in a very narrow range of coupling strength but for a global one (macroscopically) it occurs sequentially in a broad range of coupling strength preceded by an intermittent synchronization. On the other hand, in the case of mutual coupling a very large value of coupling strength is required for local synchronization and, consequently, all the local subsystems synchronize immediately for the same value of the coupling strength and hence globally synchronization also occurs in a narrow range of the coupling strength. In the transition regime, we observe a new type of synchronization transition where long intervals of high quality synchronization which are interrupted at irregular times by intermittent chaotic bursts simultaneously in all the systems, which we designate as global intermittent s

This paper deals with the chaotic oscillator synchronization. A new approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization and generalized synchronization are the particular cases of the synchronized behavior called as "time-scale synchronization". The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled Rössler systems and two coupled Chua's circuits.

Data fusion algorithms that employ LiDAR measurements, such as Visual-LiDAR, LiDAR-Inertial, or Multiple LiDAR Odometry and simultaneous localization and mapping (SLAM) rely on precise timestamping schemes that grant synchronicity to data from LiDAR and other sensors. Poor synchronization performance, due to incorrect timestamping procedure, may negatively affect the algorithms' state estimation results. To provide highly accurate and precise synchronization between the sensors, we introduce an open-source hardware-software LiDAR to other sensors time synchronization system that exploits a dedicated hardware LiDAR time synchronization interface by providing emulated GNSS-clock to this interface, no physical GNSS-receiver is needed. The emulator is based on a general-purpose microcontroller and, due to concise hardware and software architecture, can be easily modified or extended for synchronization of sets of different sensors such as cameras, inertial measurement units (IMUs), wheel encoders, other LiDARs, etc. In the paper, we provide an example of such a system with synchronized LiDAR and IMU sensors. We conducted an evaluation of the sensors synchronization accuracy and precisi

We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as well as physical couplings and unknown bounded terms. A communication layer is set in place to allow the oscillators to exchange synchronizing coupling actions through a tree-like leaderless network. In particular, we present a class of hybrid coupling rules depending only on local information to ensure uniform global practical or asymptotic synchronization, which is impossible to obtain by using the Kuramoto model customarily used in the literature. We further show that the synchronization set can be made uniformly globally prescribed finite-time stable by selecting the coupling function to be discontinuous at the origin. Novel mathematical tools on non-pathological functions and set-valued Lie derivatives are developed to carry out the stability analysis. The effectiveness of the approach is illustrated in simulations where we apply our synchronizing hybrid coupling rules to models of power grids previously used in the literature.

We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite continuously vanishing Lyapunov exponent(s)). For tent maps, a limit of stability of the synchronized state is used to locate the synchronization transition that numerically is found to be continuous. For nonidentical tent maps at the partial synchronization transition, the probability distribution of the synchronization error is shown to develop highly singular behavior. We suggest that for nonidentical Bernoulli maps (and perhaps some other discontinuous maps) partial synchronization is merely a smooth crossover rather than a well defined transition. More subtle analysis in the $d=4$ case locates the point where the synchronized state becomes stable. In some cases, however, a riddled basin attractor appears, and synchronized and chaotic behaviors coexist. We also suggest that similar riddling of a basin of attractor might take place in some extended systems where it is known as stable chaos.

We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the "effective coupling" is big compared to the common noises, the former favors and the latter hinder synchronization. On the contrary, when the coupling is small compared to the proportional noises, we find that the latter induce synchronization, optimally when their intensities are big and in the n:m synchronization ratio. Furthermore, in such case a small value of the coupling is better for synchronization. Finally, we show that synchronization, which is a global property, must not be studied via local stability such as with Lyapunov exponents.

We consider a line of three mutually coupled lasers with time delays and study chaotic synchronization of the outer lasers. Two different systems are presented: optoelectronically coupled semiconductor lasers and optically coupled fiber lasers. While the dynamics of the two systems are very different, robust synchronization of end lasers is obtained in both cases over a range of parameters. Here, we present analysis and numerical simulation to explain some of the observed synchronization phenomena. First, we introduce the system of three coupled semiconductor lasers and discuss the onset of oscillations that occurs via a bifurcation as the coupling strength increases. Next, we analyze the synchronization of the end lasers by examining the dynamics transverse to synchronized state. We prove that chaotic synchronization of the outer semiconductor lasers will occur for sufficiently long delays, and we make a comparison to generalized synchronization in driven dissipative systems. It is shown that the stability of synchronous state (as indicated by negative Lyupunov exponents transverse to the synchronization manifold) depends on the internal dissipation of the outer lasers. We next pr

We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues (EVs) of the normalized graph Laplacian concentrated around 1 are more amenable for synchronization. In the light of this condition, we review spectral properties of Cayley, quasirandom, power-law graphs, and expanders and relate them to synchronization of the corresponding networks. The analysis of synchronization on these graphs is illustrated with numerical experiments. The results of this paper highlight the advantages of random connectivity for synchronization of coupled chaotic dynamical systems.

Driven by increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators (PCOs) has gained increased popularity. However, most existing results address the local synchronization of PCOs with initial phases constrained in a half cycle, and results on global synchronization from any initial condition are very sparse. In this paper, we address global PCO synchronization from an arbitrary phase distribution under chain or directed tree graphs. Our results differ from existing global synchronization studies on decentralized PCO networks in two key aspects: first, our work allows heterogeneous coupling functions, and we analyze the behavior of oscillators with perturbations on their natural frequencies; secondly, rather than requiring a large enough coupling strength, our results hold under any coupling strength between zero and one, which is crucial because a large coupling strength has been shown to be detrimental to the robustness of PCO synchronization to disturbances.