Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

含三次耦合项的两自由度Duffing系统的共振及混沌行为

研究了一类含三次耦合项的两自由度Duffing系统的动力学行为。首先应用多尺度方法近似求解系统的一阶稳态响应。通过讨论系统的主共振和1∶1内共振,分析了三次耦合项对系统响应的影响。随后研究系统随外加周期力强度变化的分岔过程,发现除了常见的倍周期分岔通向混沌外,还存在一种直接由周期运动进入混沌的突发路径。结合对系统的最大Lyapunov指数,相轨图及Poincar啨映射的分析验证了上述结论。     

Gauss白噪声激励下分数阶导数系统的非平稳响应

研究了Gauss(高斯)白噪声激励下具有分数阶导数阻尼的非线性随机动力系统的非平稳响应.应用等价线性化方法将非线性系统转化为等价的线性系统,之后采用随机平均法获得系统响应满足的FPK(Fokker-Planck-Kolmogorov)方程,其中分数阶导数近似为一个周期函数.使用Galerkin方法求解FPK方程进而得到系统的近似非平稳响应.数值结果验证了方法的正确性和有效性.     

一类新混沌系统的线性状态反馈控制

研究了一类新混沌系统的控制问题.利用Routh-Hurwitz准则对受控系统进行了稳定性分析，结合线性状态反馈方法理论上严格证明了达到控制目标反馈系数的选择原则.数值研究证明了该方法能够有效地控制混沌系统到失稳的平衡点或周期解，同时控制效果在弱噪声干扰下具有很强的鲁棒性. 关键词： 新混沌系统 线性状态反馈控制 Routh-Hurwitz准则 噪声     

Duffing-van der Pol系统的随机分岔

应用广义胞映射图论方法(GCMD)研究了在谐和激励与随机噪声共同作用下的Duffing-van der Pol系统的随机分岔现象. 系统参数选择在多个吸引子与混沌鞍共存的范围内. 研究发现, 随着随机激励强度的增大,该系统存在两种分岔现象: 一种为随机吸引子与吸引域边界上的鞍碰撞, 此时随机吸引子突然消失; 另一种为随机吸引子与吸引域内部的鞍碰撞, 此时随机吸引子突然增大. 研究证实, 当随机激励强度达到某一临界值时, 该系统还会发生D-分岔(基于Lyapunov指数符号的改变而定义), 此类分岔点不同于上述基于系统拓扑性质改变所得的分岔点.     

Complex dynamical behavior and chaos control in fractional-order Lorenz-like systems

In this paper, the complex dynamical behavior of a fractional-order Lorenz-like system with two quadratic terms is investigated. The existence and uniqueness of solutions for this system are proved, and the stabilities of the equilibrium points are analyzed as one of the system parameters changes. The pitchfork bifurcation is discussed for the first time, and the necessary conditions for the commensurate and incommensurate fractional-order systems to remain in chaos are derived. The largest Lyapunov exponents and phase portraits are given to check the existence of chaos. Finally, the sliding mode control law is provided to make the states of the Lorenz-like system asymptotically stable. Numerical simulation results show that the presented approach can effectively guide chaotic trajectories to the unstable equilibrium points.     

表面织构对PTFE复合材料摩擦磨损行为的影响

为了研究表面织构对聚四氟乙烯(PTFE)复合材料摩擦磨损性能的影响规律及其作用机理，采用BBD响应面法对试验进行设计与分析，利用LSR-2M往复摩擦试验机测试了复合材料的摩擦学性能，建立了织构参数与摩擦系数和体积磨损率之间的二次回归模型，研究了槽宽、间距和角度参数及其交互作用对复合材料摩擦学性能的影响. 结果表明:二次回归模型显著，拟合精度分别为82.9%和83.2%，预测出槽宽323.2 μm、间距295.4 μm、角度88.7°时摩擦系数存在最小值0.147，槽宽331.1 μm、间距307.6 μm、角度87.6°时体积磨损率存在最大值8.11×10?5 mm3/(Nm)；织构增大了初始摩擦系数和体积磨损率，但有利于储存磨屑，在接触应力作用下磨屑中的纳米粒子与槽底及侧面的粗糙峰形成了机械互锁，提高了磨屑的附着力，促进了转移膜的生成.      

二阶变系数中立型时滞微分方程的振动性

研究了一类二阶变系数中立型时滞微分方程的振动性.在前人研究的基础上,通过引入函数r(t),使方程一般化,进而由构造函数法,可以得到方程(1)和(2)是振动的充分条件.结果推广并丰富了已有文献的结论.     

A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems

In this paper, a novel adaptive control approach is presented to simultaneously achieve synchronization and anti-synchronization in partially linear chaotic systems. Through appropriately separating state vectors of such systems, synchronization and anti-synchronization could be simultaneously realized in different subspaces, which may be strictly proven theoretically. Simulation results for a Lorenz chaotic system and a new hyper-chaotic system are provided to illustrate the effectiveness of the proposed method. Finally, a new secure communication scheme based on such a synchronization phenomenon of the hyper-chaotic system is demonstrated. Numerical results show success in transmitting a periodic signal with high security.     

异结构系统混沌同步的新方法

基于Lyapunov稳定性理论, 结合反馈控制和自适应控制方法, 提出了一种异结构混沌系统同步的新方法. 该方法适用范围广, 不仅能为人们提供控制器的一般选取办法，而且对于具体的误差系统还可进一步简化控制器结构, 具有稳健、易于实现等优点. 通过对Lorenz系统与Liu系统、超混沌的R?ssler系统与广义Lorenz系统的同步数值仿真, 证实了该方法的有效性. 关键词： 混沌同步 Lorenz系统 R?ssler系统 Lyapunov函数