The eight-fold way for optical quasicrystals

Network theory is increasingly employed to study the structure and behaviour of social, physical and technological systems — including civil infrastructure. Many of these systems are interconnected and the interdependencies between them allow disruptive events to propagate across networks, enabling damage to spread far beyond the immediate footprint of disturbance. In this research we experiment with a model to characterise the configuration of interdependencies in terms of direction, redundancy, and extent, and we analyse the performance of interdependent systems with a wide range of possible coupling modes. We demonstrate that networks with directed dependencies are less robust than those with undirected dependencies, and that the degree of redundancy in inter-network dependencies can have a differential effect on robustness depending on the directionality of the dependencies. As interdependencies between many real-world systems exhibit these characteristics, it is likely that many such systems operate near their critical thresholds. The vulnerability of an interdependent network is shown to be reducible in a cost effective way, either by optimising inter-network connections, or by hardening high degree nodes. The results improve understanding of the influence of interdependencies on system performance and provide insight into how to mitigate associated risks.     

耦合含时滞的相互依存网络的局部自适应异质同步

针对由两个子网络构成的耦合含时滞的相互依存网络,研究其局部自适应异质同步问题.时滞同时存在于两个子网络的内部耦合项和子网络间的一对一相互依赖耦合项中,且网络的耦合关系满足非线性特性和光滑性.基于李雅普诺夫稳定性理论、线性矩阵不等式方法和自适应控制技术,通过对子网络设置合适的控制器,提出了使得相互依存网络的子网络分别同步到异质孤立系统的充分条件.针对小世界网络和无标度网络构成的相互依存网络进行数值模拟,验证了提出理论的正确性和有效性.     

Estimating the varying topology of discrete-time dynamical networks with noise

We propose an improved method to estimate the varying topology of discrete-time dynamical networks using autosynchronization. The networks considered in this paper can be weighted or unweighted and directed or undirected, and the dynamics of each node can be nonuniform. Furthermore, we suggest using a moving-average filter to suppress the influence of noise on parameter estimation. Finally, several examples are illustrated to verify the theoretical results by numerical simulation.     

Second-Order Controllability of Multi-Agent Systems with Multiple Leaders

This paper proposes a new second-order continuous-time multi-agent model and analyzes the controllability of second-order multi-agent system with multiple leaders based on the asymmetric topology.This paper considers the more general case:velocity coupling topology is different from location coupling topology.Some sufficient and necessary conditions are presented for the controllability of the system with multiple leaders.In addition,the paper studies the controllability of the system with velocity damping gain.Simulation results are given to illustrate the correctness of theoretical results.     

一类异构多智能体系统固定和切换拓扑下的一致性分析

对包含一阶二阶智能体的异构系统有向图中的一致性问题进行研究.对该系统采用了一种线性分布式一致性协议,基于图论和矩阵分析的方法,分析了在固定和切换拓扑情况下系统获得一致性的充分条件,该条件与控制参数和通信拓扑有关.给出了固定拓扑中系统的一致平衡点,证明了仅通信拓扑中的根节点对平衡点起作用.数值仿真验证了理论分析的正确性.     

Finite-time information consensus for multi-agent systems with fixed and switching topologies

In this paper, we study the consensus problems for a group of interacting agents. First, we analytically establish the explicit expression of the consensus state for the entire group. Second, we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies. The results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights. Third, some numerical examples are provided to analyze the influencing factors of the convergence time, that is, the parameter of the particular interaction function and the algebraic connectivity of graphs. Finally, an application of the theoretical results in sensor networks is given, namely, computing the maximum-likelihood estimate of unknown parameters.     

Studies on controllability of directed networks with extremal optimization

Almost all natural, social and man-made-engineered systems can be represented by a complex network to describe their dynamic behaviors. To make a real-world complex network controllable with its desired topology, the study on network controllability has been one of the most critical and attractive subjects for both network and control communities. In this paper, based on a given directed–weighted network with both state and control nodes, a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under Kalman’s rank condition has been developed. The experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network’s dynamics and provide the evolution of network topology during the optimization process. We also find the conclusion: “the sparse networks need more control nodes than the dense, and the homogeneous networks need fewer control nodes compared to the heterogeneous” (Liu et al., 2011  [18]), is also applicable to network complete controllability. These findings help us to understand the network dynamics and make a real-world network under the desired control. Moreover, compared with the relevant research results on structural controllability with minimum driver nodes, the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes.     

Controllability of multiple qubit systems

This paper explores the problem of manipulating multiple-qubit systems when only single-qubit operations or two-qubit-interactive operations are permitted. It is demonstrated that if there exist 2 directional control Hamiltonian for each individual qubit, and one interactive Hamiltonian for each pair of qubits, then multiple qubit systems are open-loop controllable. An important observation of physical interest is emphasized: when only single-qubit operations or two-qubit-interactive operations are permitted, only n(n+3)/2 control Hamilton may guarantee open-loop controllability of n qubit systems, and n(n+3) is, in the restricted sense, also the lower limit on the number of operators needed for controllability. At last, we demonstrate that an n-quantum-dot system is open-loop controllable even when only single-qubit operations or two-qubit-interactive operations are permitted.     

Synchronization in large directed networks of coupled phase oscillators

We study the emergence of collective synchronization in large directed networks of heterogeneous oscillators by generalizing the classical Kuramoto model of globally coupled phase oscillators to more realistic networks. We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider the case of networks with mixed positive-negative coupling strengths. We compare our theory with numerical simulations and find good agreement.     

Communication on the structure of biological networks

Networks are widely used to represent interaction pattern among the components in complex systems. Structures of real networks from different domains may vary quite significantly. As there is an interplay between network architecture and dynamics, structure plays an important role in communication and spreading of information in a network. Here we investigate the underlying undirected topology of different biological networks which support faster spreading of information and are better in communication. We analyse the good expansion property by using the spectral gap and communicability between nodes. Different epidemic models are also used to study the transmission of information in terms of spreading of disease through individuals (nodes) in those networks. Moreover, we explore the structural conformation and properties which may be responsible for better communication. Among all biological networks studied here, the undirected structure of neuronal networks not only possesses the small-world property but the same is also expressed remarkably to a higher degree compared to any randomly generated network which possesses the same degree sequence. A relatively high percentage of nodes, in neuronal networks, form a higher core in their structure. Our study shows that the underlying undirected topology in neuronal networks, in a significant way, is qualitatively different from the same in other biological networks and that they may have evolved in such a way that they inherit a (undirected) structure which is excellent and robust in communication.     

Passivity analysis of coupled inertial neural networks with time-varying delays and impulsive effects

This paper is devoted to the passivity analysis of an array model for coupled inertial delayed neural networks (NNs) with impulses under different network structures, namely directed and undirected topologies. Firstly, utilising the information of eigenvectors for the directed coupling matrix, a new Lyapunov functional is constructed, by which, together with the aid of some inequality techniques and network characteristics, the two sets of sufficient criteria are established to, respectively, guarantee the strictly input passivity and strictly output passivity of the impulsive network with directed coupling. Secondly, benefited from the properties of the undirected coupling matrix, some more concise conditions that are easier to be verified for the passivities of the undirected coupled network accompanied by impulsive effects are proposed. Finally, two numerical examples are designed to execute the verification of the derived theoretical results.     

Global synchronization for a class of dynamical complex networks

This paper is concerned with the problem of global synchronization for a class of dynamical complex networks composed of general Lur’e systems. Based on the absolute stability theory and the Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions are established to guarantee global synchronization of dynamical networks with complex topology, directed and weighted couplings. Several global synchronization criteria formulated in the form of linear matrix inequalities (LMIs) or frequency-domain inequalities are also proposed for undirected dynamical networks. In order to obtain global results, no linearization technique is involved through derivation of the synchronization criteria. Numerical examples are provided to demonstrate the effectiveness of the proposed results.     

微尺度驻停气泡柔性气-液界面抗流体剪切能力

在微流控系统中,稳定、可控的柔性气-液界面可实现声流体颗粒富集、微纳操作、快速气-液反应等各种实际物理和生化应用.微流道内气-液界面的抗流体剪切能力对于增强微尺度下气-液界面的可控性具有十分重要的意义.为此,文章研究了具有高稳定性、高可控性、可阵列化的微尺度驻停气泡现象.利用嵌入局部裂隙的微流道以及与之平行的气体流道,可对驻停气泡的生成和形态进行有效调节,并利用其可控的气-液界面实现多种功能化应用.在此基础上,文章进一步研究柔性可控气-液界面的抗流体剪切能力,对形态变化中的气-液界面受力进行分析,利用仿真和实验手段研究不同状态下气-液界面的形状特征,研究不同的液体驱动压力、裂隙尺寸以及裂隙形状对气-液界面抗剪切能力的影响,并将界面的曲率半径作为气泡驻留与否的判定依据.文章对驻停气泡柔性气-液界面抗流体剪切能力的研究有助于优化其控制方法,增强其控制稳定性并拓展其潜在应用场合.      

Enhancing the capability of controlling quantum systems via ancillary systems

This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information, such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.     

Current filamentation in bistable semiconductor systems with two global constraints

The recent advent of integral circuits combining bistable semiconductor structures with a spatially distributed driving gate has opened up new possibilities for development of self-organizing active media with controllable properties which are of potential interest for neural computer technology. In the present paper the theoretical study of instabilities and current filamentation in such systems is advanced. The consideration is based on a generalized model which treats a gate driven bistable system as an extended active medium with two global constraints related to the main and gate circuits, respectively. It is shown that the presence of a spatially distributed controlling subsystem — a driving gate — leads to a new effect of transversal nonlocal coupling between system elements which acts dramatically upon the system behaviour. The results obtained in a general form regardless of the concrete semiconductor structure design are illustrated by the example of a gate-driven pnpn-structure.     

Paths to synchronization on complex networks

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.     

Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems

Admissible consensus analysis and consensualizing controller design problems for high-order linear time-invariant singular swarm systems are investigated. Firstly, by projecting the state of a singular swarm system onto a consensus subspace and a complement consensus subspace, a necessary and sufficient condition for admissible consensus is presented in terms of linear matrix inequalities (LMIs). An approach to decrease the calculation complexity is proposed, by which only three LMIs independent of the number of agents need to be checked. Then, by using the changing variable method, sufficient conditions for admissible consensualization are shown. An explicit expression of the consensus function is given, and it is shown that the modes of the consensus function can be arbitrarily placed if each agent is R$R$-controllable and impulse controllable and the interaction topology has a spanning tree. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.     

Controllability Issues for Continuous-Spectrum Systems and Ensemble Controllability of Bloch Equations

We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum, whose controllability is not well understood. We provide several mathematical answers, with discrimination between approximate and exact controllability, and between finite time or infinite time controllability: this system is not exactly controllable in finite time T with bounded controls in L ²(0, T), but it is approximately controllable in L ^∞ in finite time with unbounded controls in L^￥_loc([0,+￥)){L^{\infty}_{loc}([0,+\infty))}. Moreover, we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin + 1/2 or −1/2.     

Noise and controllability: suppression of controllability in large quantum systems

A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields such that the effect of noise is negligible on the timescale of the transformation? Complete controllability in practice requires that the effect of noise can be suppressed for an arbitrary transformation. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases, determined by the dimension of the Hilbert space representation of the algebra. We show that for large quantum systems, generic noise in the controls dominates for a typical class of target transformation; i.e., complete controllability is destroyed by the noise.     

Synchronization between Different Networks

Synchronization between two networks with different topology structures and different dynamical behaviours is studied. These two different networks are driving and responding networks, respectively. Under the preconditions that the driving network gets synchronization, we give the conditions for the responding network to be synchronized to the same dynamics as the driving network with the help of the open-plus-closed-loop method. Then a example is given to verify the validity of the theoretical results.