多重耦合振子系统的同步动力学

耦合相振子的同步研究对理解复杂系统自组织协同的涌现具有重要的理论意义.相比于传统耦合振子的两体成对耦合,多重耦合近年来得到广泛的关注.当相振子间的多重耦合机制起主要作用时,系统会涌现一系列去同步突变,这一新颖的动力学特性对理解复杂系统群体动力学提供了重要的理论启示.本文研究了平均场的三重耦合Kuramoto系统的同步动力学,发现了去同步转变具有不可逆性,并利用平均场自洽方法和无序态线性稳定性分析揭示了不可逆去同步突变的动力学机制.进一步研究发现,随着振子自然频率分布半宽度的变化,系统会经历一系列去同步驻波态的转变.在相变临界点,系统在高维相空间会通过鞍结分岔导致同步态失稳而塌缩至稳定的低维不变环面.本文的研究揭示了多重耦合函数作用的振子系统的各种协同态及其相变机制,同时可为理解其他复杂系统(如超网络结构)协同态的动力学转变提供理论借鉴.     

与相变潜热有关的铁电-顺电相界动力学及其尺寸效应

对于铁电-顺电相界的快移动，提出了相变潜热释放传导机理进行解释，并对其尺寸效应做了进一步研究.研究表明相界移动速率随体系厚度的减小而增加.理论结果与实验符合. 关键词： 铁电相变 相界动力学 相变潜热 尺寸效应     

一维有机导体的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls 相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体tetrathiafulvalene-tetracyanoquinodimethane的Peierls相变温度进行了计算.并对其金属-绝缘体相变机制进行了讨论. 关键词： 电子-声子相互作用 Peierls相变温度 一维有机导体     

冗余自由度工业机器人模糊自适应PID控制研究

为提高汽车生产中涂胶工序的工作效率和空间利用率,改善机器人避障性能,设计了一款具有7自由度的冗余度工业涂胶机器人,并对其控制方法开展研究。针对现有PID控制方法应用于非线性时变的多自由度多刚体串联式开链系统时,控制效果有限、难以达到系统精度要求等问题,基于传统PID控制和模糊自适应控制算法,提出了一种带有重力补偿的模糊自适应PID混合控制方法。该方法在对冗余度工业机器人进行动力学分析的基础上,基于牛顿-欧拉分析法建立了冗余度机器人动力学模型,基于动力学分析设计了带有重力补偿的模糊自适应参数整定PID控制策略,建立了控制器模型,通过Matlab仿真实验表明,具有模糊自适应参数整定PID控制较有重力补偿的传统PID控制具有更好的控制效果。     

统计物理的微观动力学基础

统计的基本出发点是研究系统具有的随机性,不同系统在不同情形下的宏观热力学性质起源于系统内部随机性的差异,通过对宏观热力学系统的微观非线性动力学进行研究探索，我们可以进一步更为深入地理解物态方程、相变等诸多的宏观热力学现象。本文通过哈密顿系统的非线性动力学研究，以及遍历性理论的动力学随机性研究对此问题进行了分析，研究表明，动力学系统的全局性混沌是系统统计成立的根本要素，系统的无限大自由度（热力学极限）已不是决定性的因素，人们可以在此基础上建立少自由度系统的统计力学及热力学。     

非平衡凝固与固态相变中有关形核和长大的竞争研究

非平衡凝固和固态相变作为同热力学和动力学紧密相关的复杂理论体系,在物理冶金和凝聚态物理研究领域占据重要的地位。上述非平衡过程包含形核、生长和碰撞三个微观过程,其发生和发展均由一些竞争过程伴随、辅助甚至驱动。正确理解这些竞争过程决定了能否准确描述整个非平衡过程;材料制备中,其力学和物理/化学性能的提高也归根于这些竞争的发生与发展。因此,很有必要对非平衡凝固和固态相变中的竞争现象进行研究。本综述第一部分从形核/生长类相变角度对非平衡凝固和固态相变进行了概述,并强调了伴随其发生的竞争现象。第二部分立足于经典形核理论,对有关形核热力学、动力学以及形核方式的竞争现象进行了描述。第三部分对凝固中有关热扩散和溶质扩散以及固态相变中有关界面控制和扩散控制的生长方式竞争进行了描述。第四部分对本综述进行了总结性分析和概括,并对本领域的未来发展方向进行了预测。     

基于格子Boltzmann方法的二维气泡群熟化过程模拟

Ostwald熟化(ripening)是指局部热力学平衡状态下,颗粒/液滴/气泡系统为了减小界面能而自发地进行颗粒群尺度分布调整的过程,具有重要研究价值.针对目前数值模拟研究不充分的现状,本文采用格子Boltzmann方法,对相变速率主控的二维蒸气泡系统演化开展了数值模拟研究.模拟结果与本文推导的二维气泡群演化标度律符合较好,证实了格子Boltzmann方法对复杂相变-物质输运过程捕捉的准确性.研究同时表明,蒸气泡系统演化过程中物质输运为液相压力不平衡所驱动,并且在小气泡“溃灭”过程中水动力学作用会影响气泡群半径分布函数的局部细节;气-液状态方程参数对熟化过程的影响效果分析显示,气液两相比内能差是驱动相变的核心要素,此差异越大相变速率越快,该结论进一步诠释了化学势驱动熟化过程的物理图像.     

非线性网络的动力学复杂性研究

综述了非线性网络的动力学复杂性研究在网络理论、实证和应用方面所取得的主要进展和重要成果;深刻揭示了复杂网络的若干复杂性特征与基本定量规律;提出和建立了网络科学的统一混合理论体系(三部曲)和网络金字塔,并引入一类广义Farey组织的网络家族,阐明网络的复杂性-简单性与多样性-普适性之间转变关系;揭示了网络的拓扑结构特征与网络的动态特性之间关系;建立具有长程连接的规则网络的部分同步理论并应用于随机耦合的时空非线性系统的同步;提出复杂网络的动力学同步与控制多种方法;提出若干提高同步能力的模型、方法和途径,如同步最优和同步优先模型、同步与网络特征量关系、权重作用、叶子节点影响等;提出复杂混沌网络的多目标控制及具有小世界和无标度拓扑的束流输运网络的束晕-混沌控制方法;提出集群系统的自适应同步模型及蜂拥控制方法;探讨网络上拥塞与路由控制、资源博弈及不同类型网络上传播的若干规律;揭示含权经济科学家合作网及其演化特点;实证研究并揭示了多层次的高科技企业网和若干社会网络的特点;提出一种复杂网络的非平衡统计方法,把宏观网络推进到微观量子网络。     

威耳逊的临界点相变的重正化群理论

临界现象的研究进展缓慢,６０年代实验方面的发展使人们相继建立了几个标度理论及普适性理论,并提出了标度变换概念,威耳逊一直从事量子场论的研究,对相变理论也很关注,对迹些唯象理论不满,他把量子场论中的重正化群概念应用到相变理论中,并运用标度律和普适性概念,建立了临界点的重点重正化群理论,提供了研究临界点现象的系统方法。     

高温高压下过渡金属Ru的结构相变

采用基于密度泛函理论的第一性原理和准简谐晶格动力学方法对Ru的六角密排 (hcp)、面心立方 (fcc)、体心四方 (bct) 和体心立方 (bcc) 结构的磁性、晶格结构稳定性和高温高压下的相变进行了系统的研究. 计算获得了各相结构的磁性基态及其稳定性范围, 结果表明: 零温下在计算的压力范围内, NM-hcp 结构是Ru最稳定的结构, 压力的单独作用下并没有相变的发生; NM-fcc结构是Ru的亚稳定结构, 而NM-bcc和FM-bct结构在动力学上并不稳定. 高温高压下Ru将发生从NM-hcp到NM-fcc结构的相变, 并给出了Ru的温度压力相图. 关键词： 相变 晶格稳定性 磁性 第一性原理     

Adaptive dynamical networks via neighborhood information: synchronization and pinning control

In this paper, we introduce a model of an adaptive dynamical network by integrating the complex network model and adaptive technique. In this model, the adaptive updating laws for each vertex in the network depend only on the state information of its neighborhood, besides itself and external controllers. This suggests that an adaptive technique be added to a complex network without breaking its intrinsic existing network topology. The core of adaptive dynamical networks is to design suitable adaptive updating laws to attain certain aims. Here, we propose two series of adaptive laws to synchronize and pin a complex network, respectively. Based on the Lyapunov function method, we can prove that under several mild conditions, with the adaptive technique, a connected network topology is sufficient to synchronize or stabilize any chaotic dynamics of the uncoupled system. This implies that these adaptive updating laws actually enhance synchronizability and stabilizability, respectively. We find out that even though these adaptive methods can succeed for all networks with connectivity, the underlying network topology can affect the convergent rate and the terminal average coupling and pinning strength. In addition, this influence can be measured by the smallest nonzero eigenvalue of the corresponding Laplacian. Moreover, we provide a detailed study of the influence of the prior parameters in this adaptive laws and present several numerical examples to verify our theoretical results and further discussion.     

Finite-Time Pinning Synchronization Control for T-S Fuzzy Discrete Complex Networks with Time-Varying Delays via Adaptive Event-Triggered Approach

This paper is concerned with the adaptive event-triggered finite-time pinning synchronization control problem for T-S fuzzy discrete complex networks (TSFDCNs) with time-varying delays. In order to accurately describe discrete dynamical behaviors, we build a general model of discrete complex networks via T-S fuzzy rules, which extends a continuous-time model in existing results. Based on an adaptive threshold and measurement errors, a discrete adaptive event-triggered approach (AETA) is introduced to govern signal transmission. With the hope of improving the resource utilization and reducing the update frequency, an event-based fuzzy pinning feedback control strategy is designed to control a small fraction of network nodes. Furthermore, by new Lyapunov–Krasovskii functionals and the finite-time analysis method, sufficient criteria are provided to guarantee the finite-time bounded stability of the closed-loop error system. Under an optimization condition and linear matrix inequality (LMI) constraints, the desired controller parameters with respect to minimum finite time are derived. Finally, several numerical examples are conducted to show the effectiveness of obtained theoretical results. For the same system, the average triggering rate of AETA is significantly lower than existing event-triggered mechanisms and the convergence rate of synchronization errors is also superior to other control strategies.     

Robust synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the issue of robust synchronization for a class of fractional-order chaotic and hyperchaotic systems with model uncertainties and disturbances is studied. A stability criterion for fractional-order nonlinear dynamic systems is introduced, and an adaptive scheme is contrived to accomplish synchronization of fractional-order chaotic and hyperchaotic systems. The controller contains only a single state variable, which is simple and flexible in implementation. Two corresponding numerical examples are given to confirm the theoretical results of the paper.     

冠状动脉系统高阶滑模自适应混沌同步设计

针对冠状动脉系统混沌同步问题, 系统模型受到有界但未知的不确定干扰条件下, 利用几何齐次性理论和积分滑模面设计高阶滑模自适应控制器, 使响应系统在有限时间内跟踪驱动系统, 该方法无需提前预知扰动边界. 采用Lyapunov理论对闭环系统进行分析并证明该控制器保证该系统能够在有限时间内镇定, 从仿真实验结果可以看出所设计的控制器在不确定干扰的情况下系统具有良好鲁棒性和未知参数的自适应性, 为能够有效治疗心肌梗死等冠状动脉疾病提供了一定的理论依据.     

基于简化模型与自适应滤波的车载SINS静基座快速对准

为了实现捷联惯性导航系统(Strap-down Inertial Navigation System,SINS)快速初始对准,根据已有可观测性分析结果,通过理论分析和计算得到了扩展观测量时初始对准系统最优可观测状态量组合,在此基础上简化了对准模型,建立了新的系统方程。针对载车发动机启动或其他情况导致系统噪声无法精确统计,提出了运用基于强跟踪滤波原理的自适应卡尔曼滤波(Kalman Filter,KF)算法抑制滤波发散,加快收敛速度。仿真结果表明运用简化模型和自适应滤波在系统噪声不匹配时具有更快的收敛速度和更高的对准精度,车载实验结果也表明运用简化模型和自适应滤波可以实现快速对准。     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

Synchronization of general complex networks via adaptive control schemes

In this paper, the synchronization problem of general complex networks is investigated by using adaptive control schemes. Time-delay coupling, derivative coupling, nonlinear coupling etc. exist universally in real-world complex networks. The adaptive synchronization scheme is designed for the complex network with multiple class of coupling terms. A criterion guaranteeing synchronization of such complex networks is established by employing the Lyapunov stability theorem and adaptive control schemes. Finally, an illustrative example with numerical simulation is given to show the feasibility and efficiency of theoretical results.     

Modified KdV–Zakharov–Kuznetsov dynamical equation in a homogeneous magnetised electron–positron–ion plasma and its dispersive solitary wave solutions

This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptive technique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.     

Dynamic modeling and aperiodically intermittent strategy for adaptive finite-time synchronization control of the multi-weighted complex transportation networks with multiple delays

The idea of network splitting according to time delay and weight is introduced. Based on the cyber physical systems(CPS), a class of multi-weighted complex transportation networks with multiple delays is modeled. The finite-time synchronization of the proposed complex transportation networks model is studied systematically. On the basis of the theory of stability, the technique of adaptive control, aperiodically intermittent control and finite-time control, the aperiodically intermittent adaptive finite-time synchronization controller is designed. The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays. In addition,the conditions for the existence of finite time synchronization have been discussed in detail. And the specific value of the settling finite time for synchronization is obtained. Moreover, the outer coupling configuration matrices are not required to be irreducible or symmetric. Finally, simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.