Tianping Chen
In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li} can be obtained by the results in \cite{Lu2006}.
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In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li1,Li2} and many other papers can be obtained by the results in \cite{Chen1,Chen2}. It is pointed out that QUAD condition plays important role in discussing synchronization and consensus.
Certain consensus seeking multi-agent systems can be formulated as gradient descent flows of a disagreement function. We study how known pathologies of gradient descent flows in Euclidean spaces carry over to consensus seeking systems that evolve on nonlinear manifolds. In particular, we show that the norms of agent states can diverge to infinity, but this will not happen if the manifold is the boundary of a convex set. Moreover, the system can be initialized arbitrarily close to consensus without converging to it, but this will not happen if the manifold is analytic. For analytic manifolds, c…
In this paper, we discuss distributed adaptive algorithms for synchronization of complex networks, consensus of multi-agents with or without pinning controller. The dynamics of individual node is governed by generalized QUAD condition. We design new algorithms, which can keep the left eigenvector of the adaptive coupling matrix corresponding to the zero eigenvalue invariant. Based on this invariance, various distributive adaptive synchronization, consensus, anti-synchronization models are given.
Waveform Proportionality and Taylor's Law Induced by Synchronization of Periodic and Chaotic Oscillators
本文利用耦合振荡器模型证明同步可诱导Taylor定律，强同步导致波形比例性并产生指数为2的时间与空间TL，从而可通过均值与方差的关系推断同步的存在。
In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. W…
Fixed-time cluster synchronization for complex networks via pinning control
本文研究了通过粘贴控制实现复杂网络固定时间集群同步问题，设计了简单分布式协议并证明了其有效性，获得了固定时间集群同步的充分条件。
Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
本文提出单纯复形上由单纯拉普拉斯算子导出的非线性梯度流，将网络共识与同步模型推广到任意维度，并分析其稳态稳定性及高维结构。
The theory of cointegration has been a leading theory in econometrics with powerful applications to macroeconomics during the last decades. On the other hand the theory of phase synchronization for weakly coupled complex oscillators has been one of the leading theories in physics for many years with many applications to different areas of science. For example, in neuroscience phase synchronization is regarded as essential for functional coupling of different brain regions. In an abstract sense both theories describe the dynamic fluctuation around some equilibrium. In this paper, we point out t…
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also al…
A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the ensemble is {\it not} the same as the mean of the individuals' natural frequencies. Specifically, we show that the collective frequency equals a weighted average of the natural frequencies, where the weights are given by an out-flow centrality measure that is equivalent to a reverse PageRank central…
Synchronization reveals topological scales in complex networks
研究了复杂网络中拓扑尺度与动态时间尺度之间的关系。该分析是基于一个系统的耦合振荡器的同步的全动态。在同步过程中，模块化结构对应于定义良好的社区的节点出现在不同的时间尺度，按层次的方式排序。该分析还提供了一个有用的同步动力学，复杂网络拓扑结构和谱图分析之间的联系。
Synchronization and Information Transmission in Spatio-Temporal Networks of Deformable Units
我们研究了同步和信息交换速率之间的关系在一个时空网络，描述了经典粒子的动力学下的基板Remoissenet-Peyrard潜在的节点之间。我们还展示了如何在这个网络中检测相位和完全同步。在这样的网络中检测相位同步的困难出现，由于粒子动力学的高度非相干特性，这无法正确定义的相位动力学。检测完全同步的困难出现由于空间特性的潜在的结果在一个渐近状态高度依赖于初始状态。
Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we propose an ensemble order parameter(EOP) equation that enables us to grasp the essential low-dimensional dynamical mechanism of the explosive synchronization in heterogeneous networks. Dif- ferent solutions of the EOP equation build correspondences with diverse collective states, and different bifurcations reveal various transitions among these collective states. The structural relationship between the incoherent state and synchronous state leads to different routes of transitions to synchronization, …
Stochastic stability of continuous time consensus protocols
本文提出统一框架研究连续时间一致性协议的收敛性与随机稳定性，通过图论谱性质（如代数连通度、有效电阻）和几何性质（如循环子空间维度）刻画稳定性，并指出扩展图等稀疏高连通图在大规模网络中保持高性能。
This study is focused on the mechanisms of rhythmogenesis and robustness of anti-phase bursting in half-center-oscillators (HCOs) consisting of two reciprocally inhibitory coupled neurons. There is a growing body of experimental evidence that a HCO is a universal building block for larger neural networks, including central pattern generators (CPGs) controlling a variety of locomotion behaviors in spineless animals and mammals. It remains unclear how CPGs achieve the level of robustness and stability observed in nature. There has been a vastly growing consensus in the community of neurophysiolo…
Consensus Formation Among Mobile Agents in Networks of Heterogeneous Interaction Venues
本研究提出移动智能体在异构交互场所网络中的共识形成模型，推导有效动力学方程，发现增加密度、网络异构性和智能设计可促进凝聚力，并应用于脑同步和意见动力学。
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