Modeling mobile ad hoc communication networks on two-dimensional square lattice

In this paper, we model the mobile ad hoc communication network on a two-dimensional square lattice. Both structure and function of it depend on transmission range and site-occupancy of nodes. Critical occupancies σ_c for different transmission ranges r to maintain global connection are found. Universal scaling function behaves as η~f(R^βσ), where R=(r−r₀)/r₀, and the scaling exponent β=−0.61, which distinguishes itself from percolation in previous lattice or network models. When the occupancy σ is near the threshold σ_c, individual nodes self-organize into a dynamic small world network relative to geometric distance. The network has a cut-off degree below which clustering coefficient keeps constant, which distinguish itself from other systems and has its potential application in technical designs.     

基于量子远程传态的无线自组织量子通信网络路由协议

针对复杂结构的无线量子通信网络,提出了无线自组织量子通信网络概念并设计其路由协议．该路由协议为按需路由协议,路由度量基于相邻节点问的纠缠粒子对数目．需要发送携带信息的量子态的节点发起路由请求和建立过程,由目的节点根据路由度量选择路径．目的节点选择路径后,沿所选路径发送路由应答信息至源节点并通知路径中其他节点．信息传输过程中,若所选路径中相邻节点问无线信道或者量子信道中断,将重新发起一个路由发现过程．建立新路由．路径中节点收到路由应答信息后,利用纠缠交换和两端逼近方法,从路径两端向中间节点方向进行纠缠交换,建立量子信道后,通过量子远程传态传输携带信息的量子态,从而实现无线自组织量子通信网络中任意两节点问信息的传递．     

Explosive synchronization in network of mobile oscillators

Recently, the explosive synchronization (ES) has attracted great interests. Motivated by the recent dynamic framework of complex network, we focus on the network of mobile oscillators and study synchronization phenomenon. The local synchronous order parameter of the neighbors of the oscillator is used as the controllable variable to adjust the coupling strength of the oscillator. Hence, it can be seen as a kind of adaptive strategy. By numerical simulation, we find that ES can be observed in the dynamic network of mobile oscillators, accompanying with hysteresis loop, as the coupling strength increases gradually. It is found that the critical value of coupling strength and hysteresis loop width is affected by the natural frequency distribution and the number of neighbors the oscillator owning. It can be deduced that ES will be motivated by increasing the number of oscillators in the network. Meanwhile, our results are feasible to different natural frequency distributions, such as Lorentzian, Gaussian power-law, and Rayleigh distribution, whether it is symmetric or not.     

Explosive synchronization of complex networks with different chaotic oscillators

Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Gómez-Garden es J,Gómez S,Arenas A and Moreno Y 2011 Phys.Rev.Lett.106 128701] and chaotic oscillators [Leyva I,Sevilla-Escoboza R,BuldúJ M,Sendin a-Nadal I,Gómez-Garden es J,Arenas A,Moreno Y,Gómez S,Jaimes-Reátegui R and Boccaletti S 2012 Phys.Rev.Lett.108 168702].Here,we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks.The continuous transition is discovered for Rssler systems in both of the above complex networks.However,explosive transitions take place for the coupled Lorenz systems,and the main reason is the abrupt change of dynamics before achieving complete synchronization.Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.     

Preferential survival in models of complex ad hoc networks

There has been a rich interplay in recent years between (i) empirical investigations of real-world dynamic networks, (ii) analytical modeling of the microscopic mechanisms that drive the emergence of such networks, and (iii) harnessing of these mechanisms to either manipulate existing networks, or engineer new networks for specific tasks. We continue in this vein, and study the deletion phenomenon in the web by the following two different sets of websites (each comprising more than 150,000 pages) over a one-year period. Empirical data show that there is a significant deletion component in the underlying web networks, but the deletion process is not uniform. This motivates us to introduce a new mechanism of preferential survival (PS), where nodes are removed according to the degree-dependent deletion kernel, D(k)∝k^−α, with α≥0. We use the mean-field rate equation approach to study a general dynamic model driven by Preferential Attachment (PA), Double PA (DPA), and a tunable PS (i.e., with any α>0), where c nodes (c<1) are deleted per node added to the network, and verify our predictions via large-scale simulations. One of our results shows that, unlike in the case of uniform deletion (i.e., where α=0), the PS kernel when coupled with the standard PA mechanism, can lead to heavy-tailed power-law networks even in the presence of extreme turnover in the network. Moreover, a weak DPA mechanism, coupled with PS, can help to make the network even more heavy-tailed, especially in the limit when deletion and insertion rates are almost equal, and the overall network growth is minimal. The dynamics reported in this work can be used to design and engineer stable ad hoc networks and explain the stability of the power-law exponents observed in real-world networks.     

Route selection for interference minimization to primary users in cognitive radio ad hoc networks: A cross layer approach

An opportunistic routing problem in a cognitive radio ad hoc network is investigated with an aim to minimize the interference to primary users (PUs) and under the constraint of a minimum end-to-end data rate for secondary users (SUs). Both amplify-and-forward (AF) and decode-and-forward (DF) relaying techniques are considered for message forwarding by SU nodes in the network. Unlike popular transmit power control based solutions for interference management in cognitive radio networks, we adopt a cross layer approach. The optimization problem is formulated as a joint power control, channel assignment and route selection problem. Next, closed form expression for transmission power is derived and corresponding channel selection scheme and routing metric are designed based on this solution. The proposed route selection schemes are shown to depend not only on gains of the interference channels between SUs and PUs but also on the values of the spectrum sensing parameters at the SU nodes in the network. Two distributed routing schemes are proposed based on our analysis; (i) optimal_DF and (ii) suboptimal_AF. The routing schemes could be implemented using existing table driven as well as on demand routing protocols. Extensive simulation results are provided to evaluate performance of our proposed schemes in random multihop networks. Results show significant reduction in PUs’ average interference experience and impressive performance as opportunistic routing schemes can be achieved by our schemes compared to traditional shortest path based routing schemes. Performance improvement is also reported over prominent recent schemes.     

States and transitions in mixed networks

A network is named as mixed network if it is composed of N nodes, the dynamics of some nodes are periodic, while the others are chaotic. The mixed network with all-to-all coupling and its correspond- ing networks after the nonlinearity gap-condition pruning are investigated. Several synchronization states are demonstrated in both systems, and a first-order phase transition is proposed. The mixture of dynamics implies any kind of synchronous dynamics for the whole network, and the inixed networks may be controlled by the nonlinearity gap-condition pruning.     

振幅耦合动态网络中相邻结点间的相同步

研究用适当的量化指标来刻画动态网络的相同步,为此定义了新的量化指标:相邻结点的网络平均锁相值和网络平均相频差.动态网络结点选择的是多旋转中心的Lorenz混沌振子,对Lorenz系统进行柱面坐标变换,用振幅耦合方法构造动态网络.分别对星形网络和小世界网络进行了仿真计算,结果表明随着耦合强度的增大,网络中相邻结点的两个系统之间存在相同步现象,而且相同步行为与定义的量化指标之间存在较准确的对应关系.     

复杂网络上的部分同步化:奇异态、遥同步与集团同步

近年来,复杂网络上耦合振子的部分同步化引起了人们极大的关注,其潜在或背后的原因是部分同步化斑图在大脑网络中广泛存在,并很可能与大脑的认知或记忆等功能有密切的联系.本文对这些进展进行简单的总结与归纳,并按照学者们研究的不同侧重点,将其分成三方面来进行介绍,即奇异态、遥同步与集团同步化.着重强调这三种情形各自出现的条件、常用的研究模型、检测的方法以及侧重解释的生物现象等方面.并对它们三者之间的相互关系及今后的研究方向做一些简单的探讨.     

Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris--Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.     

Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular (clustered) property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra- coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network. Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.     

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper,the pinning synchronization problem of stochastic delayed complex network (SDCN) is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller,where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller,some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.     

A fault-tolerant small world topology control model in ad hoc networks for search and rescue

Due to their self-organized, multi-hop and distributed characteristics, ad hoc networks are useful in search and rescue. Topology control models need to be designed for energy-efficient, robust and fast communication in ad hoc networks. This paper proposes a topology control model which specializes for search and rescue—Compensation Small World-Repeated Game (CSWRG)—which integrates mobility models, constructing small world networks and a game-theoretic approach to the allocation of resources. Simulation results show that our mobility models can enhance the communication performance of the constructed small-world networks. Our strategy, based on repeated game, can suppress selfish behavior and compensate agents that encounter selfish or faulty neighbors. This model could be useful for the design of ad hoc communication networks.     

Phase synchronization on small-world networks with community structure

In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.     

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

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.     

结点含时滞的具有零和非零时滞耦合的复杂网络混沌同步

时滞耦合的复杂网络同步已经有大量的研究成果,而网络结点含时滞的无时滞耦合的复杂网络同步的研究工作较少.为使网络模型更接近现实和适用更广的范围,建立了网络结点含时滞,而耦合兼零时滞(无时滞)和非零时滞(有时滞)的复杂网络同步模型.在网络结点上分别设置线性控制器和自适应控制器,研究了其混沌同步问题.利用李雅普诺夫稳定性定理,设计相应的正定函数,分别给出了复杂网络同步的充分条件.最后,为证实同步方案的有效性,选择时滞Logistic函数为结点动力系统,在兼无时滞和有时滞的网络上,给出了线性反馈控制同步误差数值演化趋势.     

一种有效的提高复杂网络同步能力的自适应方法

本文提出了一种根据节点状态来调节网络中边权重的自适应方法(MDMF)来提高网络的同步能力, 总结了网络规模与网络平均速度对同步能力的影响. 研究发现, 通过这种自适应方法, 得到网络的同步能力与网络规模成幂率关系. 在相同网络规模下, 此方法能使网络的同步能力高于无权重网络几个数量级.当网络规模越大时, 提高同步能力越高效.