Undercompressive shocks for nonstrictly hyperbolic conservation laws

We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems.     

非线性碰摩力对碰摩转子分叉与混沌行为的影响

研究了具有非线性碰摩力的转子局部碰摩的分叉与混沌运动,利用计算机仿真对某发动机转子的碰摩故障进行了数值模拟,讨论了转子系统参数的变化对转子混池运动状态的影响,并与碰摩实验结果进行了比较,发现了具有非线性碰摩力的转子局部碰摩转子系统的各种多周期运动和混沌运动及其演变过程。     

关于一类扰动系统的极限环上界问题

本文讨论了一类扰动系统在其一阶Ｍｅｌｎｉｋｏｖ函数恒为零,而二阶Ｍｅｌｎｉｋｏｖ函数不恒为零时的Ｐｏｉｎｃａｒｅ分支及Ｈｏｐｆ分支的有关问题,得到了该系统的极限环个数的上界估计,本文推广并深化了文「４」的结论,也弥补了该文的某些不足。     

具有全局中心的三次Hamilton系统的Poincaré分支

本文讨论一类具有全局中心的三次:Hamilton系统的Poincare分支,证明了 其Poincare分支最多可以产生两个极限环,而且可以产生两个极限环.     

迭代微分方程解的存在性及分支

本文讨论迭代微分方程ｘ（ｔ）＝ｆ（ｘ（ｔ），ｘ（ｘ（ｔ）））的解的性态，并在ｆ（ｘ（ｔ），ｘ（ｘ（ｔ）））＝（ｘ＾２（ｔ）－μ）ｘ（ｘ（ｔ））时研究解的分支问题，更正了现有文献中的错误，结出了正确，完整的结果。     

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.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

耦合混沌系统的相同步：从高维混沌到低维混沌

混沌系统的相同步现象是近几年混沌同步研究的热点,它反映了混沌运动中的有序行为.用分岔树来研究耦合系统相同步的进程,并用Lyapunov指数谱来探讨系统动力学在相同步时从高维混沌向低维混沌过渡的进程.发现了从多个有理同步的时间交替到完全相同步的道路.还 发现了相同步中的混沌抑制及通过倍周期分岔向混沌同步的恢复.此外,研究表明,非对称 耦合可以大大加强耦合系统的相同步,这对实际应用有重要的意义. 关键词： 相同步 分岔树 李指数     

有界随机噪声激励下软弹簧Duffing振子的安全盆分叉

研究了软弹簧Duffing振子在有界随机噪声激励下，系统安全盆的侵蚀现象，并提出了随机安全盆分叉的概念. 计算表明，由于随机扰动的影响，系统的随机安全盆分叉点发生了偏移. 关键词： Duffing振子 有界随机噪声 安全盆 分叉     

Equilibrium points and bifurcation control of a chaotic system

Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.