Chaotic-to-ordered state transition of cathode-sheath instabilities in DC glow discharge plasmas

Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical DC glow discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of the discharge glow and shows a period subtraction of order 7 period → 5 period → 3 period → 1 period, i.e. the system goes to single mode through odd cycle subtraction. On further increasing the discharge voltage, the system goes through period doubling, like 1 period → 2 period → 4 period. On further increasing the voltage, the system goes to stable state through two period subtraction, like 4 period → 2 period → stable.     

Complex Behaviors of a Simple Traffic Model

In this paper, we propose a modified traffic model in which a single car moves through a sequence of traffic lights controlled by a step function instead of a sine function. In contrast to the previous work [Phys. Rev. E 70 (2004)016107], we have investigated in detail the dependence of the behavior on four parameters, ω, α, η, and a1, and given three kinds of bifurcation diagrams, which show three kinds of complex behaviors. We have found that in this model there are chaotic and complex periodic motions, as well as special singularities. We have also analyzed the characteristic of the complex period motion and the essential feature of the singularity.     

横向补给系统高架索的稳定性与分岔研究

考虑集中质量对系统动力学行为的影响,建立了横向补给系统高架索振动的理论模型.利用Galerkin方法和多尺度方法对动力学方程进行渐近分析.通过对系统Jacobi矩阵特征值的讨论,分析了系统的稳定性.根据系统渐近解的消除永年项条件,得到了系统的振幅分岔方程.借助Mathematica软件,对系统的局部分岔行为进行研究,得到了系统的转迁集以及相应的局部分岔图,研究表明横向补给系统高架索的振动中存在的多种分岔现象.     

互联网时滞对偶拥塞控制模型动力学特征的分析与计算

以互联网拥塞控制的一种时滞对偶改进模型为研究对象,应用标准形理论、中心流形定理和霍普夫分岔理论,从动力学角度研究互联网拥塞控制的分岔与稳定性分析方法.研究表明,模型的分岔与稳定性主要由通信时延决定,当通信时延超过临界值时模型产生分岔现象,使互联网的链路代价函数发生振荡.并得到该模型的分岔方向及分岔周期解等动力学特征的定量计算公式,为时滞对偶模型的设计提供理论依据.研究结论概括为两个定理,其正确性得到计算机仿真验证.     

The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant

In this paper, the extended Pad'e approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter varepsilon is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.     

Dynamic bifurcation of a modified Kuramotoben Sivashinsky equation with higher-order nonlinearity

Under the periodic boundary condition, dynamic bifurcation and stability in the modified Kuramoto—Sivashinsky equation with a higher-order nonlinearity μ(u_x)^pu_xx are investigated by using the centre manifold reduction procedure. The result shows that as the control parameter crosses a critical value, the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points. Furthermore, for cases in which the distances to the bifurcation points are small enough, one-order approximations to the bifurcation solutions are obtained.     

倒摆运动的混沌行为

设计一个受周期外力驱动的倒摆实验装置,并建立该系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法求解非线性方程并判断解的性质．通过改变系统参数,画出时域图、相图及分岔图,计算分析和实验发现,这个简单的力学系统存在十分丰富的动力学行为（分岔、混沌）．理论分析、数值模拟和实验结果一致．     

Bifurcation Instability of sheet metal during spring-back

In automotive and home appliance industries, there are many complex-shaped sheet metal components which need to be fabricated in multiple stamping operations. For example, the manufacturing of an outer case of washing machine consists of stamping followed by a bending operation. After the first stage of the stamping process, a large amount of spring-back takes place, and therefore, it is difficult to proceed to the next stage of the bending process. In the stamping process of that kind of sheet component with low geometric constraint, the forming area is large compared to the forming depth. Therefore, the formed part is in an unstable state and is less geometrically constrained, which causes a large amount of spring-back. To investigate this phenomenon, finite element analyses are carried out. During a spring-back analysis after forming, bifurcation takes place and the finite element solution procedure using the Newton–Raphson scheme becomes unstable. To get a stable post-bifurcation solution, a bifurcation algorithm is introduced at the bifurcation point. The deformed shapes obtained from finite element analyses are in good agreement with the experimental data. From this study, it is shown that the bifurcation behaviour enlarges the spring-back and the degree of dimensional error. To obtain additional possible post-bifurcation solutions, non-bifurcation analyses using initial guesses obtained in a modal analysis are carried. For the initial guesses, lowed four eigenmodes are utilized. Finally, the post-bifurcation behaviour and spring-back amount are investigated for various process parameters including the forming depth, punch width and corner radius.     

参外联合激励复合非线性振子的分岔分析

讨论了参外联合激励复合非线性振子的动力学行为.对其定常解在一阶近似下的方程进行了局部分岔分析,给出了简单分岔和Hopf分岔发生的条件,并通过对近似方程和原系统的数值模拟加以验证.分析了多种参数对该振子动力学行为演化过程的影响.根据全局分岔理论探讨了该振子在不同条件下发生同宿、异宿分岔的必要条件,其结论与数值计算的结果大致符合. 关键词： 复合非线性振子 局部分岔 全局分岔 混沌     

一类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower和Holling-IV类功能性反应函数的时滞捕食系统,讨论了该系统的局部稳定性和Hopf分支存在性, 并利用中心流形定理和规范型理论确定了Hopf分支的方向和分支周期解的稳定性.仿真实例证明了理论分析结果的正确性.