Basins of Attraction of Periodic Oscillations in Suspension Bridges

We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations.     

银川市区地震地质条件与城市规划中的防震问题

论述了银川地堑新生代的基本构造特征；对银川市区附近的地震地质环境和活动断层分布以及历史上遭遇过的地震灾害特点进行了分析．在此基础上就银川市城市发展规划中应注意的防震问题提出了建议     

开关广义Mandelbrot集

基于开关复映射,阐述了开关广义Mandelbrot集(简称广义M集)的构造方法,并构造出一系列开关广义Mandelbrot集·在对开关映射作用下复C平面上初始点轨道的分析及开关广义M集构造算法研究的基础上,通过计算机实验,得出以下结论:①开关广义M集具有分形结构;②开关广义M集包含了构成开关映射的两个映射的部分稳定区;③开关广义M集的演化过程依赖于相角主值范围的选取     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

Noninvertibility and the structure of basins of attraction in a model adaptive control system

Summary We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.     

基于GIS的河道、蓄滞洪区洪水演进动态可视化仿真研究

结合地理信息系统(GIS)技术和三维仿真图示技术,探讨了基于GIS的河道、蓄滞洪区洪水演进可视化仿真技术原理与方法,分析了洪水演进可视化模型的建立过程,设计出河道、蓄滞洪区洪水演进系统的总体结构及开发模式,并介绍了系统具体功能的实现.本仿真模型在实例中得到了成功的应用,可为防洪减灾决策提供快捷、直观形象的信息支持.     

祁连山北麓挤压隆起山地边缘不对称地堑发育模式研究

根据构造、沉积和地貌的野外调查与新分析研究了河西走廓压性山地边缘发育的一种特殊的活动构造地貌－喇叭形不对称地堑。它在呈弧形的山地边缘平面上为喇叭形河口，实际上是发育在特定的构造部位、由断层围限的不对称地堑。     

A new two-point scheme for multiple roots of nonlinear equations

In most of the earlier research for multiple zeros, in order to obtain a new iteration function from the existing scheme, the usual practice is to make no change at the first substep. In this paper, we explore the idea that what are the advantages if the flexibility of choice is also given at the first substep. Therefore, we present a new two-point sixth-order scheme for multiple roots (m>1). The main advantages of our scheme over the existing schemes are flexibility at both substeps, simple body structure, smaller residual error, smaller error difference between two consecutive iterations, and smaller asymptotic error constant. The development of the scheme is based on midpoint formula and weight functions of two variables. We compare our methods with the existing methods of the same order with real-life applications as well as standard test problems. From the numerical results, we find that our methods can be considered as better alternates for the existing methods of the same order. Finally, dynamical study of the proposed schemes is presented that confirms the theoretical results.     

Macroscopic traffic models: Shifting from densities to “Celerities”

The advent of techniques to measure velocities of “GPS equipped vehicles” using satellite technology, replacing the density of the road traffic sensors, motivates and justifies the revision of conceptual, mathematical algorithms and software based models. This paper summarizes studies on the traffic evolutions achieving the minimum of a congestion function controlled “macroscopic traffic velocities” called “celerities” instead of founding traffic regulation on the measures of traffic densities. The flux valued function is the Fenchel transform of the fundamental diagram and is a convex decreasing function. We use the properties of capture basins investigated in viability theory, specifically a Lax-Hopf formula characterizing them and the “Max-Plus” morphism of capture basins for deriving the statements proved in this paper. Traffic conditions involve as well boundary conditions or conditions on trajectories inside the domain.     

Coexistence of domains of attraction of nonautonomous neural networks with time-varying delays

This paper presents new dynamical behavior, i.e., the coexistence of 2^N domains of attraction of N-dimensional nonautonomous neural networks with time-varying delays. By imposing some new assumptions on activation functions and system parameters, we construct 2^N invariant basins for neural system and derive some criteria on the boundedness and exponential attractivity for each invariant basin. Particularly, when neural system degenerates into periodic case, we not only attain the coexistence of 2^N periodic orbits in bounded invariant basins but also give their domains of attraction. Moreover, our results are suitable for autonomous neural systems. Our new results improve and generalize former ones. Finally, computer simulation is performed to illustrate the feasibility of our results.