三种单节点摄动对混合值逻辑网络极限集的影响  

THREE TYPES OF FUNCTION PERTURBATIONS OF MIX-VALUED LOGICAL NETWORKS WITH IMPACTS ON LIMIT SETS

作　　者：贾光钰 冯俊娥[1] 

机构地区：[1]山东大学数学学院,济南250100

出　　处：《系统科学与数学》2016年第3期426-436,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(61374025);山东省杰出青年基金项目(JQ201219)资助课题

摘　　要：研究了三种单节点摄动对混合值逻辑网络不动点和极限环的影响.受布尔网络单节点摄动的启发,文章首先在结构矩阵的基础上提出了混合值逻辑网络中单节点摄动的定义,并利用矩阵半张量积的方法得到了单节点摄动下混合值逻辑网络的代数形式.然后,研究了结构矩阵与状态转移矩阵间的关系,并提出了三种特殊类型的单节点摄动.最后,得到了三种单节点摄动对混合值逻辑网络的不动点及极限环影响的充分必要条件.This paper investigates three types of function perturbations and their impacts on the fixed points and limit cycles of mix-valued logical networks. Motivated by the concept of one-bit perturbation in Boolean networks, the definition of general perturbation in mix-valued logical networks is presented and the algebraic expression of the perturbed networks can be given by applying semi-tensor product （STP） of matrices. Three kinds of function perturbations are given and their impacts on fixed points and limit cycles are discussed by analyzing the changes of transition matrix in the algebraic form.

关 键 词：矩阵半张量积(STP) 混合值逻辑网络 单节点摄动 不动点 极限环. 

分 类 号：O157.5[理学—数学]