Quasi-synchronization of fractional-order complex networks with random coupling via quantized control

We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.

Controlling chaos to unstable periodic orbits and equilibrium state solutions for the coupled dynamos system

In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle＇s invariance principle is used to control chaos to unstable equilibrium （i.e. saddle point, focus, node, etc.）. The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS

This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.

Outer synchronization between two different fractional-order general complex dynamical networks

Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order a can be chosen appropriately to adjust the synchronization effect effectively.

Generalized projective synchronization of fractional-order complex networks with nonidentical nodes

This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.

耦合发电机系统的动力学分析及其自适应控制

利用相图、庞加莱截面、功率谱、时间序列图分析了耦合发电机系统的混沌吸引子的特点、对称性、平衡点及稳定性等基本动力学特性。提出了在目标态未知的情况下利用自适应反馈法将混沌系统精确地控制到不稳平衡点,并给出了理论证明,数值模拟验证了该方法的有效性和可行性。

调节L2增益抑制耦合发电机组的混沌现象

耦合发电机系统在一定条件下出现混沌,它可能导致系统失控,使系统彻底崩溃.当系统存在不确定因素干扰时,提出了L2性能准则控制方法:使耦合发电机系统渐近稳定和进行干扰抑制.然后采用非线性系统无源化方法设计混沌系统的反馈控制律,利用L2增益进行干扰抑制.最后计算机仿真证明该方法的有效性.

关于暴时电离层电流分布的南北半球不对称性

采用国际上广泛认可的高层大气和电离层经验模式提供的各种参数，通过电离层电流连续方程，计算出强磁暴条件下6月至日和12月至日内，磁纬±72°和磁地方时00：00-24：00之间电离层电场、电流等的分布,计算中考虑了地磁和地理坐标间的偏离；除中性风场感生的发电机效应外，还包含了磁层耦合（极盖区边界的晨昏电场和二区场向电流）的驱动外源．结果表明，6月至日时，磁层扰动自极光区向中低纬的穿透情况在南、北半球内基本接近，北半球内略强；但12月至日时，呈现明显的不对称性，南半球的电流穿透远强于北半球，而电场的穿透则是在北半球更强．无论南北半球，在中高纬地区，午夜至黎明时段出现较强的东向电场分量。其E×B的向上漂移效应，正是解释我们以往不少研究现象中所期盼的物理机制．

地球内核与地球深部动力学

地球内核由外核富含铁元素的液态物质结晶而成。经证实，内核正以约１（°）／ａ的速率相对于地幔向东转动。内核的旋转是通过穿过内核的地震波的走时随时间变化推测得到的。这种变化是最近十多年来揭示出的内核各向异性在空间方位的改变所造成。内核的各向异性被认为起因于各向异性的铁晶体的有序排列，但这种有序排列的机制还不清楚。内核在地球发电机中起着重要的作用。利用大型的并行计算机，人们已得到能产生像地磁场一样的三维发电机数值模拟。地震学观测到的内核差速旋转为最近的发电机数值模拟提供了支持。这种数值模拟曾预测：导体内核与外核产生的磁场的电磁耦合驱动了内核每年几度向东旋转。地核通过核幔边界的接触及内核与地幔的引力耦合与地幔存在强烈的相互作用。多学科领域的突破为认识地球的深部动力过程提供了极好的机会和手段。

磁层-电离层电动耦合的中纬电离层效应

本文通过对1982年磁扰期间琼中、北京两站地磁X分量变化的分析,证实了磁层-电离层电动耦合对中纬电离层电流的影响.分析发现:磁静、磁扰条件下的平均日变化中,两站X分量变化在白天有反向的趋势.这表明它们分处于与动力效应对应的电离层发电机电流圈中心之南北两侧.在磁暴主相期间,X分量变化形态与之明显不同,两站地磁南北分量有同向变化,且变幅相近,甚至有时北京站△X更大.对环电流能量增长指数R小于—25nT/h的21次事件所作的时序叠加分析(以R最负时为零时)进一步证明,这种同向变化是普遍存在的.两站零时之△X大小相近,相关系数高达0.98.该同向变化与R指数突然变负密切相关. 以上对比表明,与发电机电流造成两站X分量反向变化不同,同向变化是磁层源高纬扰动电流向中低纬直接穿透的结果.本文对动力和电动耦合两种过程的不同进行了初步讨论.

一个新的超混沌耦合发电机系统及其超混沌控制

在三维耦合发电机系统的基础上,引入非线性控制器,构建一个新的超混沌耦合发电机系统,分析了新系统平衡点的性质、Lyapunov指数谱、吸引子的相图等动力学特性;利用线性反馈控制法,通过设计合适的反馈增益,实现了新系统的超混沌控制.理论分析和数值仿真验证了该方法的有效性.

用非相干散射雷达链的观测资料研究高、低纬电离层间的耦合

本文用美国NCAR非相干散射雷达链的观测资料进行了两个事例分析。结果表明,在所选事例的中、弱磁扰期间,高低纬电离层间以动力耦合效应为主,即扰动电离层发电机的特征较明显。由于赤道电离层特性和赤道站雷达观测灵敏度较高,从而也观测到与扰动电场从高纬直接穿透过来相关的电动耦合现象。最后,对有关的物理过程进行了讨论。

磁层-电离层-热层耦合的模式计算和分析

对磁层-电离层电动耦合和电离层发电机两种效应进行了模式计算,并对所得的一些耦合现象作了综合讨论.结果表明,在中低纬和赤道区的电离层和地磁研究中必须考虑磁层-电离层耦合效应向中低纬区的穿透和屏蔽;潮汐发电机效应对极光区(电导率增高时)的作用也值得重视.这两效应的特征和相对重要性随磁暴的发展阶段而异,在高低纬区也各不相同,但都有明显的晨昏不对称性.此外,弱磁扰对中低纬电离层形态的影响也不容忽视.

耦合发电机系统的周期反馈控制研究

针对耦合发电机系统的混沌特性,给出了一种强度周期反馈控制器,实现了耦合发电机系统的混沌控制.该控制方法能将耦合发电机混沌系统控制到某一平衡态或周期态.数值仿真证明了该方法的有效性.

不确定变形耦合发电机系统的参数辨识与自适应同步

研究了不确定变形耦合发电机系统的自适应同步和参数辨识,设计了自适应控制器和参数更新规则,理论证明了该控制器可使得两个变形耦合发电机系统——驱动系统和未知参数的响应系统渐进地达到同步,并且可以辨识出响应系统的未知参数.数值模拟结果证明了该控制器的有效性.

超混沌耦合发电机系统与超混沌Lü系统的异结构同步

研究了超混沌耦合发电机系统与超混沌Lü系统的异结构同步问题。根据Lyapunov稳定性理论,设计了合适的控制函数,构建异结构同步误差系统的Lyapunov函数,从理论上证明了该方法的可行性;数值模拟结果验证了该方法的有效性。

参数未知的超混沌系统的反同步与参数辨识

基于混沌同步的主动控制法,提出反对称结构的直接构造法,利用该方法设计了反同步控制器和参数追踪规则,构建了反同步控制器的电路实验,实现了参数未知的超混沌耦合发电机系统的反同步与未知参数的辨识。数值模拟和电路仿真结果证明了该方法的有效性。

用改良单反馈法实现损耗型变形耦合发电机系统的混沌控制

采用常规线性反馈法对一个考虑机械阻尼损耗的耦合发电机系统实施混沌控制,从操作性强、利于实现和降低控制功率等方面考虑,提出一种改良线性反馈法.即仅当运动轨道接近控制目标时才实施控制,最大限度地维持系统动力学特性不变.此方法具有滑模控制作用,可以调整极限环半径等系统性态.基于Lya-punov指数和Routh-Hurwitz判据,讨论受控系统的混沌轨道达到不稳平衡点或极限环的条件,给出理论上的证明.最后,通过数值模拟验证方法的有效性.

变形耦合发电机混沌系统的追踪控制

针对变形耦合发电机混沌系统的结构特点,设计统一形式的非线性追踪控制器。根据非线性系统的线性化稳定理论,对系统同步误差稳定性进行分析和证明。这里所设计的控制器可以实现变形耦合发电机系统的状态变量与任意给定参考信号的广义同步。以追踪常值信号、周期信号和混沌信号为例,进行数值仿真,进一步表明该控制方法的有效性。