Adaptive algorithms for synchronization, consensus of multi-agents and anti-synchronization of direct complex networks

Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. The collective phase sensitivity and collective phase coupling functions, which quantitatively characterize the macroscopic rhythms, are illustrated using three representative models of limit-cycle oscillators. As an important result of the theory, we demonstrate noise-induced anti-phase synchronization between macroscopic rhythms by direct n…

Anti-phase synchronization of phase-reduced oscillators using open-loop control

In this letter, we present an elegant method to build and maintain an anti-phase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The anti-phase synchronization is achieved using a common input that couples the oscillators and consists of a sequence of square pulses of appropriate amplitude and duration. This example provides a proof of principle that open-loop control can be used to create desired synchronization patterns for nonlinear oscillators, when feedback is expensive or impossible to obtain.

Symmetries and synchronization in multilayer random networks

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…

Consensus seeking gradient descent flows on boundaries of convex sets

Consensus on nonlinear spaces is of use in many control applications. This paper proposes a gradient descent flow algorithm for consensus on hypersurfaces. We show that if an inequality holds, then the system converges for almost all initial conditions and all connected graphs. The inequality involves the hypersurface Gauss map and the gradient and Hessian of the implicit equation. Moreover, for the inequality to hold, it is necessary that the manifold is the boundary of a convex set. The literature already contains an algorithm for consensus on hypersurfaces. That algorithm on any ellipsoid i…

群体 Swarmalators 中的反相同步

Anti-phase synchronization in a population of swarmalators

研究了被划分为不同社区的 swarmalators 群体在空间与相位交互强度变化下的集体动力学，发现社区间相位耦合强度的不同会导致静态同步、反相同步及类嵌合体共存状态，并给出了半解析证明。

Synchronization and Anti-synchroniztion of Dynamically Coupled Networks

We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a small percentage of the total number of nodes. We demonstrate that the dynamics of the mean field for a single network has an equivalent description in terms of a Langevin equation for a particle in a double-well potential. The coupling of two networks or equivalent coupling of two Langevin equations demonstrates synchronization or antisynchronization between t…

单纯复形上的共识，或：非线性单纯拉普拉斯算子

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。

First-order route to antiphase clustering in adaptive simplicial complexes

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in which the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning …

Anticipating synchronization with machine learning

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to…

网络中振子同步的反脆弱性与损伤响应

Antifragility and response to damage in the synchronization of oscillators on networks

本文引入数学框架评估Kuramoto模型耦合振子系统中连边权重降低对同步的影响，通过数值分析揭示反脆弱响应机制，为定量探索复杂系统反脆弱性提供通用方法。

Collective frequency variation in network synchronization and reverse PageRank

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…

通过粘贴控制实现复杂网络固定时间集群同步

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。