Abstract. In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based manipulating (CBM) method, where the node centrality is measured by the well-known PageRank algorithm. Extensive numerical simulation on many modeled networks demonstrated that the CBM method is more effective in facilitating synchronization than the degree-based manipulating method and the random manipulating method for adding or removing links. The reason is that the CBM method can effectively narrow the incoming degree distribution and reinforce the hierarchical structure of the network. Furthermore, we apply the CBM method to the links rewiring procedure where at each step one link is removed and one new link is added. The CBM method helps to decide which links should be removed or added. After several steps, the resulting networks are very close to the optimal structure from the theoretical analysis and the evolutionary optimization algorithm. The numerical simulations on the Kuramoto model further demonstrate that our method has an advantage in shortening the convergence time to synchronization on directed networks. Full paper： http://stacks.iop.org/1367-2630/14/083006
在 https://www.simics.net/mwf/topic_show.pl?tid=24312 (只有注册用户可以访问)中提到All function and method calls to a given device instance in Simics are designed to be atomic. The only way to force Simics to violate this is to call other functions or methods from within the first call.。 翻译过来就是：在Simics中，一个给定设备实例的所有的函数和方法调用都被设计成原子的。破坏Simics的原子性的唯一办法就是在这个函数中调用其它的函数和方法。 这样Simics中的原子性问题，或者同步问题就被轻松地解决了。在Simics中可以放心地让多个主(host)对一个设备进行操作。
PRL 98, 034101 (2007) Abstract: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. 这篇文献，我没有仔细地阅读，但也有粗略的观感如下： 1.Kuramoto 模型，研究了ER和SF两种拓扑结构的网络，在由完全非同步向完全同步转化过程中的差异。这种转化过程是发生时，网络拓扑结构是静态的，但耦合的强度是改变的。据了解，这个思路也不是第一次出现在这篇文章中。 2.利用KM模型的相对简单特性，给出了 关于全局和局域同步范围的量度r，rlink。这样的思路，如何体现在一个具体一些极限环模型中呢？即在其他模型中如何定义这两个量度？如果说KM就抽象可以代表所有极限环振子系统，那么对于相位不是那么方便定义的混沌振子系统，如Lronz系统，这种方法还如何办呢？ 3.In the presence of hubs, a giant component of synchronized pairs of oscillators forms and grows by recruiting nodes linked to them.这说明了了hubs结点在同步过程中的作用。 4.我感兴趣的是给定一个耦合强度，如果在完全非同步的初始状态下，向可能的同步状态演化过程中hubs结点的作用是不是与本文所述的一样呢？
Chaos 16, 015104 (2006) Changsong Zhou and Jurgen Kurths 这是一篇我看到的极出色的文章，所研究的复杂网络上的分层同步（我就直译了）问题对识别网络的拓扑结构具有启发性。PRE80，016116（2009）也正是基于此，明确提出了用来网络探测。在没有看到更早的文献之前，我先当它是利用动力学来探测网络度分布的第一文了。如此说，EPL82，68001（2008）可能要觉得有点冤，因为那里宣称是首次。但在仔细阅读这三文章之后，我还是认为这里闪烁的原创性更明亮！ 文章的摘要：We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. 1.在简介里隐约给出了复杂网络的研究对象主要就是指联接，或称为复杂的拓扑结构。而对于结点的研究则是动力学的范围。所以是否可以将我们研究的对象分为这么两层次：复杂系统是第一层、复杂网络与动力系统（微分动力系统）是第二层，这一层是拓扑结构与单一结点动力学。在第二层次上的单独研究都已经开展得很多了，而第一层的研究则包括常见的什么传播动力学、网络同步等。 2.MSF分析的是网络的完全同步（CS），但是网络的最自然状态往往是非完全同步的。在这种情况下，局部群体行为的分析也是十分令人感兴趣的。这对应以往斑图研究中的发达湍流与全局同步运动（规则斑图之一）之间的状态。当然以前斑图研究的也可以说成是简单连接的网络上的动力学研究。 3.Interestingly, the stability analysis of the CS state can be adopted to provide an understanding of the hierarchical synchronization.这是在简介结尾时说的一句话，可能是对应II（E）部分的，平均场分析。因为这一部分的分析方法与MSF相似。不同的是normalized耦合强度是结点度的显函数，且由之可知度大的结点耦合强度也大。所以可想而知的是有权连接对所讨论的对象也有很大的影响。 4.文章最后一句Our present interest is on self-organization of structures and dynamics due to the interplay between them令人浮想连翩。 5.总体还有个感觉就是工作量很大，做得很细，值得学习。
这是一篇PRE 80， 030624（2009）的文章，作者为Liang Huang等。 摘要：Master-stability functions （MSFs） are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators. 1. The MSF can be obtained independent of the topoloty of the underlying network that supports a large number of such oscillators.这是否意味着，我们没办法用MSF方法来讨论具体一个网络中，某些特定的点对稳定同步的作用呢？如度数最大的点，n个点构成的团簇等子网络等。 2.A necessary condition ofr synchronization to occur is that the MSF be negative and the corresponding normalized coupling parameters fall in the negative region of the MSf. 这将意味着存在某类动力系统，其特定拓扑结构的网络，用MSF分析可以完全同步，但实际上却不可能同步。这篇文章说的都是成功的例子，可曾有实例反倒？ 3.由normalized parameter引起的：正则（canonical）、正规(normal，regular)、重整(renormal)、归一之间的关系问题。汉语对应翻译是不是有点乱？ 4. For nonlinear oscillators, the Jacobian matrix DF typically depends on the trajectory S(t). 这里没有指出同步解S（t）是唯的，所以当非线性振子是多稳振子时，MSF应用时会是怎么样的呢？这可不可以作为问题2的一个回答？因为可能对一个稳态是可同步的，另一个稳态是不可同步的。如果两个态都是稳定同步态，系统最终选择哪个稳定性也要取决于初始条件。 5.The Turing bifurcation 看到这个词颇感亲切，当年做复杂系统中的斑图嘛！但发现图3的最后一个图，可能是作者没画全吧？当K进一步增大时Phsi要小于0才行呢。（从表中可知，的确如此） 6.synchronization 在这里指完全同步，而且说一个系统是不是同步的，指的是非完全同步状态作为初始状态，或完全同步状态下给一定的扰动后，系统还能不能再同步。那么如Rossler等方便定义相位的系统，其在一定情况下出现的相同步能不能用MSF方法来讨论？ 7.因为最大李指数与单一动力系统的动力学、normalized参数有关，那在动力系统与耦合强度都确定的情况下，是否存在不同类型的拓扑结构，会使得处于临界状态的网络由可同步切换到不可同步，或相反呢？ 8. 第四部分的讨论， 是否可以用数值模拟进行验证？
标签: synchronization
