Synchronization in complex networks of phase oscillators: A survey

The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.     

Semi‐global and global containment control of multi‐agent systems with second‐order dynamics and input saturation

This paper considers both semi‐global and global containment control for a second‐order multi‐agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi‐global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M‐matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Synchronization of Instantaneous Coupled Harmonic Oscillators With Communication and Input Delays

This paper investigates the synchronization issue of instantaneous coupled harmonic oscillators with communication and input delays. A distributed synchronization algorithm is proposed for such oscillator systems, and some general algebraic criteria on exponential convergence are established for the algorithm. The main contributions of the present investigations include: (i) the directed network topology is first considered in the case of instantaneous interaction; (ii) both the time‐varying communication and input delays are simultaneously addressed; (iii) the effects of communication and input delays on synchronization performance of coupled harmonic oscillators are discussed. It is shown the communication delays have a more important impact than the input delays on determining synchronization dynamics of coupled harmonic oscillators. Explicitly, in absence of communication delays, coupled harmonic oscillators can achieve synchronization oscillatory motion, whereas, so long as communication delays are nonzero at infinite multiple impulsive times, its synchronization (or consensus) state is zero. Finally, numerical examples demonstrate the obtained theoretical results.     

Phase synchronizing in Hindmarsh-Rose neural networks with delayed chemical coupling

Although diffusive electrical connections in neuronal networks are instantaneous, excitatory/inhibitory couplings via chemical synapses encompass a transmission time-delay. In this paper neural networks with instantaneous electrical couplings and time-delayed excitatory/inhibitory chemical connections are considered and scaling of the spike phase synchronization with the unified time-delay in the network is investigated. The findings revealed that in both excitatory and inhibitory chemical connections, the phase synchronization could be enhanced by introducing time-delay. The role of the variability of the neuronal external current in the phase synchronization is also investigated. As individual neuron models, Hindmarsh-Rose model is adopted and the network structure of the electrical and chemical connections is considered to be Watts-Strogatz and directed random networks, respectively.     

Influence of temperature on the liver circadian clock in the ruin lizard Podarcis sicula

Reptiles represent an interesting animal model to investigate the influence of temperature on molecular circadian clocks. The ruin lizard Podarcis sicula lives in a continental climate and it is subjected to wide range of environmental temperatures during the course of the year. As consequence, ruin lizard daily activity pattern includes either the hibernation or periods of inactivity determined by hypothermia. Here we showed the rhythmic expression of two clock genes, lPer2 and lClock, in the liver of active lizards exposed to summer photo-thermoperiodic conditions. Interestingly, the exposition of lizards to hypothermic conditions, typical of winter season, induced a strong dampening of clock genes mRNA rhythmicity with a coincident decrease of levels. We also examined the qualitative and quantitative distribution of lPER2 and lCLOCK protein in different cellular compartments during the 24-h cycle. In the liver of active lizards both proteins showed a rhythmic expression profile in all cellular compartments. After 3 days at 6 degrees C, some temporal fluctuations of the lCLOCK and lPER2 are still detectable, although, with some marked modifications in respect to the values detected in the liver of active lizards. Besides demonstrating the influence of low temperature on the lizard liver circadian oscillators, present results could provide new essential information for comparative studies on the influence of temperature on the circadian system across vertebrate classes.     

低压引弧性能的研究

针对弧焊电源存在的高频引弧的干扰和接触引弧的电极损耗问题，提出一种新型的引弧方法－低压引弧，并对低压引弧电路及其原理进行分析，实验结果表明，该种方法引弧性能良好，提高了弧焊电源的可靠性。     

变频移相混合式控制CLL谐振变换器

为适应宽范围输入电压场合,该文结合变频控制(variable frequency control,VFC)和移相控制(phase shift control,PSC)这2种控制方式的特点,提出在输入高压时变换器进行移相控制,输入低压时进行变频控制的混合式控制方法。详细分析了在2种不同模式控制下全桥CLL谐振变换器的原理以及特性,并对变换器的谐振网络参数进行合理的设计。以500 W原理样机为例,对混合式控制全桥CLL谐振变换器进行实验验证。实验结果表明在混合控制策略下,全桥CLL谐振变换器能够实现原边开关管的零电压开通(zero voltage switching,ZVS)和副边整流二极管的零电流关断(zero-current switching,ZCS),并具有开关频率变化范围窄、效率高等特点。     

Consensus reaching in multi-agent packet-switched networks with non-linear coupling

An important task for multi-agent systems (MAS) is to reach a consensus, e.g. to align their velocity vectors. Recent results propose appropriate consensus protocols to achieve such tasks, but most of them do not consider the effect of communication constraints such as the presence of time-delays in the exchange of information between the agents. In this article, we provide conditions for a non-linear, locally passive MAS of arbitrary size to reach a consensus, when the agents communicate over a packet-switched network that is characterised by a given topology. Both the cases of constant and switching topologies are considered. The nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution. We first embed this model in another, distributed but deterministic delay model and provide conditions for the error introduced by this simplification. In our main result, we provide conditions for the locally passive MAS with distributed delays to reach a consensus. In the case of a fixed topology, the underlying directed graph has to contain a spanning tree. In the case of a switching topology, only the union graph of all graphs that persist over time is required to contain a spanning tree. These conditions are independent of the distribution and the size of the packet delays. To show attractivity of the consensus set, we use an invariance principle for systems described by functional differential equations based on an appropriate Lyapunov–Razumikhin function. This methodological approach is the main contribution of this work and can also be applied to other consensus problems with delays. We illustrate our results by numerical simulations showing synchronisation of non-linear Kuramoto oscillators over a digital network.     

混沌振子实现微弱周期小信号的检测

通过对混沌振子Duffing方程及其检测原理的介绍,发现混沌振子对周期小信号具有敏感特性,能够在强噪声环境下实现对微弱周期小信号的检测。Matlab实验仿真和分析证明了采用混沌振子Duffing检测微弱周期小信号的可行性。     

An Adaptable Oscillator-Based Controller for Autonomous Robots

This paper proposes a unique oscillator-based robot controller with learning abilities to effectively guide a team of robots operating in uncertain environments. To verify this, we designed four separate controllers and compared their performance in a series of tests in several different environments. The experiments used a team of three robots to explore arenas with variable lighting and different obstacle patterns, with a goal of having the team as a whole absorb as much light as possible. The four controllers were: a reactive controller, an oscillator with fixed parameters, an oscillator whose parameters changed based on the pattern of sensor information received, and an oscillator-based controller that used reinforcement learning. Experiments confirmed that the proposed method outperforms the others in all environments tested. This material is based upon work supported in part by the U.S. Army Research Office under grant/contract number DAAG55-98-1-0011.