Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

改进的最小费用理论在盲竖井选址中的应用

在网络的任意点求解绝对中心等特殊点是网络流研究的一个难点.在目前最小费用理论的基础上引入平面几何理论,把网络等效于几何图形,建立了数学模型.通过求解,得出了网络间的最佳连接点,从而确定出盲竖井的位置.最后以云南锡业集团个旧东区两个生产平台之间的连接为一算例,得出了理想的结果,验证了该方法的有效可行性.     

AC 1 make or break lemma

Mañé suggested the following question: Consider aC ^r flow on a compact manifold without boundary and suppose that the ω-limit set of a pointp intersets the α-limit set ofq, i.e. ω(p)∩α(q)≠Ø. Can the flow beC ^r-perturbed so that either (a)p is connected toq (p andq in the same orbit) or (b) ω(p)∩α(q)=Ø for the new flow? Here we solve positively a stronger version of this problem forC ¹ small perturbations of the original flow.     

Connecting orbits among Denjoy minimal sets for monotone twist map

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action.     

用升降法求95连杆疲劳极限的探讨

为了较精确地求出95连杆的疲劳极限,本文将在材料疲劳试验中应用较广的升降法推广应用于连杆,给出了用升降法求构件疲劳极限的基本过程。文中首先选取了试验的控制因素并确定了连杆的控制点(应力被选定为控制应力的点定义为控制点)。然后在四级应力水平下进行了连杆的疲劳试验,并以最大应力幅点的应力为计算应力求出了连杆的疲劳极限。     

THE EXISTENCE OF CONNECTING ORBITS

In this paper,using the notion of an isolating block and Conley's attractor theory,an existence criterion of trajectories connecting a pair of invariant sets of ordinary differential equations is given.     

基于收益共享机制的干支线衔接运输联合定价模型

在班轮运输网络中,支线运输与干线运输具有互补性,干线承运人与支线承运人之间的合作能够为托运人提供更高的便利度和更完善的运输服务。本文在考虑可替代运输路径之间竞争关系的基础上,研究干支线衔接路径的定价问题,在运输链纵向一体化和分散化两种结构下,构建Bertrand博弈模型研究上下游承运人的均衡运价。同时,设计合理的收益共享机制,使承运人在分散结构的运输系统中仍能实现运输链的协调。     

Numerical computation of viscous profiles for hyperbolic conservation laws

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterization of the heteroclinic manifold which can be understood as a generalized phase condition; in the case of shock profiles, this phase condition has a natural interpretation regarding their stability. We prove that our method converges and present numerical results for several systems of conservation laws. These examples include traveling waves for the Navier-Stokes equations for compressible viscous, heat-conductive fluids and for the magnetohydrodynamics equations for viscous, heat-conductive, electrically resistive fluids that correspond to shock wave solutions of the associated ideal models, i.e., the Euler, resp. Lundquist, equations.

     

Isolating block and existence of connecting orbits

Using the notion of an isolating block, some existence criteria of trajectories connecting two critical pints of planar dynaniiral systems are given. Project supported by the National Natural Science Foundation of China.     

由一类非线性常微分方程的抛物线解所确定的扭波

通过求解与平面动力系统的两个平衡点相连接的抛物线解,获得了6种非线性行波方程的扭波解存在条件,并给出了这些扭波解的参数表达式,以及上述解存在的参数条件．