A RESEARCH ON PHASE SYNCHRONIZATION FOR EXTENDED KURAMOTO MODEL

This paper discuses three types of phase synchronization phenomena in extended Kuramoto model. A certain quadratic form is applied to analyze the stability of phase synchronization manifolds without any stability knowledge for error systems. Some simple and convenient criteria are obtained for these types of phase synchronization. Also, the effectiveness of the proposed criteria is illustrated successfully by an example.     

Observer-based lag synchronization between two different complex networks

In this paper, some new criteria for lag synchronization between two or more complex networks are proposed based on the theory of state observer. Some adaptive controllers are designed to make the drive and response systems achieve lag synchronization, no matter whether the nodes in the two systems are with the same dynamical character or the coupling configuration matrices are nonidentical. In addition, based on the output coupling, the amount of coupling variables between two connected nodes is flexible, which can save a lot of channel resources, simplify the network topology and has more significant meanings in engineering applications. At last, the effects of the lag synchronization criteria are verified through some simulation experiments.     

Circuit realization,chaos synchronization and estimation of parameters of a hyperchaotic system with unknown parameters

In this article, the adaptive chaos synchronization technique is implemented by an electronic circuit and applied to the hyperchaotic system proposed by Chen et al. We consider the more realistic and practical case where all the parameters of the master system are unknowns. We propose and implement an electronic circuit that performs the estimation of the unknown parameters and the updating of the parameters of the slave system automatically, and hence it achieves the synchronization. To the best of our knowledge, this is the first attempt to implement a circuit that estimates the values of the unknown parameters of chaotic system and achieves synchronization. The proposed circuit has a variety of suitable real applications related to chaos encryption and cryptography. The outputs of the implemented circuits and numerical simulation results are shown to view the performance of the synchronized system and the proposed circuit.     

Robust H_∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with exter- nal disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchro- nized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.     

Collective dynamics in a non-dissipative two-coupled pendulum system

We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Fu~.hermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincar6 sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.     

Exponential synchronization of chaotic Lur’e systems with time-varying delay via sampled-data control

In this paper, we study the exponential synchronization of chaotic Lur＇e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov-Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequal- ities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.     

COMPASS time synchronization and dissemination—Toward centimetre positioning accuracy

In this paper we investigate methods to achieve highly accurate time synchronization among the satellites of the COMPASS global navigation satellite system (GNSS). Owing to the special design of COMPASS which implements several geo-stationary satellites (GEO), time synchronization can be highly accurate via microwave links between ground stations to the GEO satellites. Serving as space-borne relay stations, the GEO satellites can further disseminate time and frequency signals to other satellites such as the inclined geo-synchronous (IGSO) and mid-earth orbit (MEO) satellites within the system. It is shown that, because of the accuracy in clock synchronization, the theoretical accuracy of COMPASS positioning and navigation will surpass that of the GPS. In addition, the COMPASS system can function with its entire positioning, navigation, and time-dissemination services even without the ground link, thus making it much more robust and secure. We further show that time dissemination using the COMPASS-GEO satellites to earth-fixed stations can achieve very high accuracy, to reach 100 ps in time dissemination and 3 cm in positioning accuracy, respectively. In this paper, we also analyze two feasible synchronization plans. All special and general relativistic effects related to COMPASS clocks frequency and time shifts are given. We conclude that COMPASS can reach centimeter-level positioning accuracy and discuss potential applications.     

Explosive synchronization: From synthetic to real-world networks

Synchronization is a widespread phenomenon in both synthetic and real-world networks. This collective behavior of simple and complex systems has been attracting much research during the last decades. Two different routes to synchrony are defined in networks; first-order, characterized as explosive, and second-order, characterized as continuous transition. Although pioneer researches explained that the transition type is a generic feature in the networks, recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization. The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions. Despite different theoretical analyses about the appearance of the first-order transition, studies are limited to the mean-field theory, which cannot be generalized to all networks. There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization, e.g., the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks. In this review article, explosive synchronization is discussed from two main aspects. First, pioneer articles are categorized from the dynamical-structural framework point of view. Then, articles that considered different oscillators in the explosive synchronization frameworks are studied. In this article, the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators. Also, efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.     

Measure synchronization in hybrid quantum-classical systems

Measure synchronization in hybrid quantum-classical systems is investigated in this paper. The dynamics of the classical subsystem is described by the Hamiltonian equations, while the dynamics of the quantum subsystem is governed by the Schrödinger equation. By increasing the coupling strength in between the quantum and classical subsystems, we reveal the existence of measure synchronization in coupled quantum-classical dynamics under energy conservation for the hybrid systems.     

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.