几个映射类的半群结构及性质  

Semigroup structures and properties of some kinds of mappings

作　　者：李翠萍[1] LI CuiPing

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《中国科学：数学》2017年第1期135-146,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:61134005);中央院校基础科研业务费(批准号:30458805和30459201)资助项目

摘　　要：本文考虑人口动力学中的几类常见的重要映射,如logistic映射:f(x)=rx(1-x)(x∈R,r>0为参数)和具有Allee效应的单峰Allee映射、Sigmoid映射等;研究这几类映射的某些性质(如不动点的个数、位置及其稳定性等)在复合运算下的可保持性;证明这些映射在复合运算下是封闭的,即它们构成半群,并给出例子说明理论结果.In this paper, we consider several kinds of maps frequently appearing in the population dynamics, e.g., logistic mapping： f（x） = rx（1 - x） （x ∈ R, r 〉 0 is a parameter）, unimodel Allee maps with Allee effect and Sigmoid mapping, etc. We study the persistence of some properties for these maps such as the numbers of fixed point, their positions, stabilities and so on. We prove that they are closed under composition of maps. That means they form a semigroup. The examples are given to illustrate the results.

关 键 词：适应性函数 Allee映射 周期差分方程 

分 类 号：O152.7[理学—数学]