具有离散性的连续性模型映射

为了实现在连续性空间中的离散分段问题,采用解决离散性问题的方法虚拟构造连续性集合,将连续性问题映射为分段的离散问题,根据集合中元素的离散特性实现连续性模型的分段求解.通过数据结构的设计与压缩路径的算法证实,模型的映射能够解决实际问题的分段求解.     

Periodicity and map for discovery of new ionic liquids

1 Introduction In undertaking the researches on ionic liquids, we wished to establish periodicity and draw a “map” of ionic liquids for providing definite guidance to dis-cover, design, and choose the proper ionic liquids to meet the specific applicatio…     

Bifurcations and chaos of a discrete mathematical model for respiratory process in bacterial culture

The discrete mathematical model for the respiratory process in bacterial culture obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, condition of existence of chaos in the sense of Marotto＇s definition of chaos is proved. The bifurcation diagrams, Lyapunov exponents and phase portraits are given for different parameters of the model, and the fractal dimension of chaotic attractor was also calculated. The numerical simulation results confirm the theoretical analysis and also display the new and complex dynamical behaviors compared with the continuous model. In particular~ we found that the new chaotic attractor, and new types of two or four coexisting chaotic attractors, and two coexisting invariant torus.     

Rank deficiency and superstability of hybrid systems

The objectives of this paper are to study the rank properties of flows of hybrid systems, show that they are fundamentally different from those of smooth dynamical systems, and to consider applications that emphasize the importance of these differences. It is well known that the flow of a smooth dynamical system has rank equal to the space on which it evolves. We prove that, in contrast, the rank of a solution to a hybrid system, a hybrid execution, is always less than the dimension of the space on which it evolves and in fact falls within possibly distinct upper and lower bounds that can be computed explicitly. The main contribution of this work is the derivation of conditions for when an execution fails to have maximal rank, i.e., when it is rank deficient. Given the importance of periodic behavior in many hybrid systems applications, for example in bipedal robots, these conditions are applied to the special case of periodic hybrid executions. Finally, we use the rank deficiency conditions to derive superstability conditions describing when periodic executions have rank equal to 0, that is, we determine when the execution is completely insensitive to perturbations in initial conditions. The results of this paper are illustrated on three separate applications, two of which are models of bipedal walking robots: the classical single-domain planar compass biped and the two-domain planar kneed biped.     

A map describing EEG activity of human brain

A model of electrical activity of human brain considered as a complex dynamical system is given based on the EEG time series. The model fits the data remarkably well. The predictive ability of the model is limited to a few time steps as expected for a chaotic time series.     

On Colimits in Categories of Relations

We study (finite) coproducts and colimits of -chains in Rel(C), the 2-category of relations over a given category C. The former exist and are the same as in C provided that C is extensive. The latter do not exist for example in Rel(Set). However, the canonical construction of those colimits in the category of sets can be generalized to Rel(Set). The canonical cocone is shown to satisfy a 2-categorical universal property, namely that of an lax adjoint cooplimit. Sufficient conditions for any base category C to admit the construction are given.A necessary and sufficient condition for the construction to yield colimits of -chains in the category of maps of Rel(C) is also given.     

环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

两自由度塑性碰撞振动系统的动力学研究

用三维映射表示具有单侧刚性约束的两自由度振动系统在塑性碰撞时的动力学方程。借助理论分析与数值方法研究了系统周期n-1振动的存在性与稳定性，描述了系统周期n-1振动的特点，讨论了碰撞振子与约束擦边引起的Poincare映射奇异性对系统全局分岔的影响。     

柱面上有根近三角剖分的计数

柱面上的三角剖分是一类与环面上的地图紧密相关的地图．本文提供了一个计算柱面上有根近三角剖分的具有三个变量的精确公式．