Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation

This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.     

Routing strategies in traffic network and phase transition in network traffic flow

The dynamics of information traffic over scale-free networks has been investigated systematically. A series of routing strategies of data packets have been proposed, including the local routing strategy, the next-nearest-neighbour routing strategy, and the mixed routing strategy based on local static and dynamic information. The capacity of the network can be quantified by the phase transition from free flow state to congestion state. The optimal parameter values of each model leading to the highest efficiency of scale-free networked traffic systems have been found. Moreover, we have found hysteretic loop in networked traffic systems with finite packets delivering ability. Such hysteretic loop indicates the existence of the bi-stable state in the traffic dynamics over scale-free networks.      

四角点简支双稳态层合板振动特性研究

双稳态层合板作为一种柔性可变体结构,为实现振动状态下的构型调控,将对其开展固有振动特性的 研究．本文以四角点简支约束的矩形非对称铺设双稳态板作为研究对象,运用最小势能原理、一阶剪切变形理 论、以及冯卡门几何非线性位移应变关系,得到双稳态板的两种稳态构型．首次给出了适合于四点简支的6参 数构型函数与17参数构型函数,研究对比发现对于稳态构型采用17参数的构型函数结果相对更精确;对于应 用线性位移应变关系的基于任一稳态构型下振动固有特性而言,这两种构型函数得到的结果基频相差2 %,其 它阶次频率相差也不大．随后采用6参数构型函数得到的稳态构型研究了几何尺寸、铺层数分别对两种稳态构 型固有振动特性的影响．本研究对于进一步研究该类结构动态跳变机理具有重要意义．     

非对称铺层复合材料层合板的双稳态特性半解析研究

非对称铺层的复合材料层合板在存在热残余应力的情况下，具有双稳态性质．层合板的两个稳态之间仅需要一个适当的激励就可以互相转化，因此该结构在变体飞机上应用广泛．基于经典层合板理论，本文引入几何大变形建立了具有双稳态性质的复合材料层合板的能量泛函，提出了一个高阶的位移场函数，用瑞利里兹法推导出一组关于位移场函数系数的非线性方程组．结合牛顿迭代法和消元法求解非线性方程组，得到了层合板面外位移场．同时利用有限元软件ABAQUS，对复合材料层合板双稳态机理进行了数值模拟．选取了几组具有代表性的铺层进行计算，以有限元结果为基准，比较了本文的位移场结果与前人的结果，验证了高阶位移场函数的准确性．     

PYRAMIDAL TRAVELING FRONTS OF BISTABLE REACTION-DIFFUSION EQUATIONS WITH DELAY

This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.     

液晶光学双稳态装置

介绍用液晶作为非线性元件构建的光学双稳态装置，该装置结构简单，使用可靠，实验内容丰富，适合教学要求。     

Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra

We derive a lower bound for energies of harmonic maps of convex polyhedra in to the unit sphere S² with tangent boundary conditions on the faces. We also establish that C maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent maps of finite energy.This revised version was published online in March 2005 with corrections to the cover date.     

动载荷作用下中介轴承的非线性热行为研究

中介轴承作为双转子系统高低压转子重要的支承部件,其内圈和外圈均随着低压转子和高压转子高速旋转, 其传热问题更加突出.本文研究中介轴承在非线性动载荷作用下的非线性热行为.基于双转子系统动力学响应定义中介轴承动载荷,考虑中介轴承的径向游隙、分数指数非线性和参数激励等非线性因素,中介轴承动载荷会出现跳跃和双稳态等非线性行为. 考虑润滑剂的黏温关系,根据Palmgren经验公式建立动载荷作用下中介轴承的热传递模型,通过数值求解得到中介轴承稳态温度,发现动载荷的非线性行为导致中介轴承温度出现跳跃和双稳态等非线性热行为.分析转速比、偏心距、中介轴承径向游隙、Hertz接触刚度和滚子数目对中介轴承温度及非线性热行为的影响,表明偏心距、径向游隙和刚度只影响非线性热行为,而转速比和滚子数目对两者都有重要影响. 本文研究表明,动载荷相较于静载荷更适合描述中介轴承的实际载荷,由于双转子系统具有非线性振动特性, 中介轴承的热行为也表现出复杂的非线性行为.      

NONLINEAR THERMAL ANALYSIS FOR THE INTER-SHAFT BEARING UNDER THE DYNAMIC LOAD 1)

中介轴承作为双转子系统高低压转子重要的支承部件,其内圈和外圈均随着低压转子和高压转子高速旋转, 其传热问题更加突出.本文研究中介轴承在非线性动载荷作用下的非线性热行为.基于双转子系统动力学响应定义中介轴承动载荷,考虑中介轴承的径向游隙、分数指数非线性和参数激励等非线性因素,中介轴承动载荷会出现跳跃和双稳态等非线性行为. 考虑润滑剂的黏温关系,根据Palmgren经验公式建立动载荷作用下中介轴承的热传递模型,通过数值求解得到中介轴承稳态温度,发现动载荷的非线性行为导致中介轴承温度出现跳跃和双稳态等非线性热行为.分析转速比、偏心距、中介轴承径向游隙、Hertz接触刚度和滚子数目对中介轴承温度及非线性热行为的影响,表明偏心距、径向游隙和刚度只影响非线性热行为,而转速比和滚子数目对两者都有重要影响. 本文研究表明,动载荷相较于静载荷更适合描述中介轴承的实际载荷,由于双转子系统具有非线性振动特性, 中介轴承的热行为也表现出复杂的非线性行为.     

双稳态系统中随机共振和相干共振的相关性

研究了加性噪声和乘性噪声共同驱动的双稳态系统中的随机共振和相干共振现象. 针对加性噪声和乘性噪声之间不存在关联性和存在关联性两种情形, 引入一种适当的能同时表征随机共振和相干共振的指标, 应用一阶欧拉方法, 通过数值模拟对系统的随机共振和相干共振现象进行研究. 结果表明在弱噪声驱动下, 随着加性噪声强度的增加, 当系统出现相干共振时, 如果给系统外加一个弱周期驱动力, 几乎在同一时刻, 系统也出现了随机共振现象; 但随着乘性噪声强度的增加, 仅当加性噪声和乘性噪声之间相关时, 此结论成立. 并且系统参数对相干共振和随机共振的影响是一致的. 关键词： 双稳态系统 随机共振 相干共振