概率级联布尔网络的集镇定及其应用  

Set stabilization of probabilistic cascading Boolean networks and its applications

作　　者：丁雪莹 李海涛[1] DING Xue-ying;LI Hai-tao(School of Mathematics and Statistics,Shandong Normal University,Jinan Shandong 250014,China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250014

出　　处：《控制理论与应用》2019年第2期271-278,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(61374065;61503225);山东省自然科学基金项目(ZR2015FQ003;JQ201613)资助~~

摘　　要：随着系统生物学和医学的迅速发展,基因调控网络已经成为一个热点研究领域.布尔网络作为研究生物系统和基因调控网络的一种重要模型,近年来引起了包括生物学家和系统科学家在内的很多学者的广泛关注.本文利用代数状态空间方法,研究了概率级联布尔网络的集镇定问题.首先给出概率级联布尔网络集镇定的定义,并利用矩阵的半张量积给出了概率级联布尔网络的代数表示.其次基于该代数表示,定义了一组合适的概率能达集,并给出了概率级联布尔网络集镇定问题可解的充要条件.最后将所得的理论结果应用于概率级联布尔网络的同步分析及n人随机级联演化布尔博弈的策略一致演化行为分析.With the rapid development of systems biology and medical science, gene regulatory networks have become a heated research field. As an important model for studying biological systems and gene regulatory networks, in the past few decades, Boolean networks have attracted extensive attention from many scholars including biologists and system scientists. This paper studies the set stabilization problem of probabilistic cascading Boolean networks (PCBNs). Firstly, the concept of set stabilization of PCBNs has been proposed, and the considered PCBN is converted to an equivalent algebraic form by using the semi-tensor product of matrices. Secondly, based on the equivalent algebraic form, a series of probabilistic reachable sets is defined and a necessary and sufficient condition is presented for the set stabilization of PCBNs. Finally, as applications of set stabilization of PCBNs, the synchronization of PCBNs and strategy consensus of n-person random cascading evolutionary Boolean games are investigated, respectively, and several necessary and sufficient conditions are presented.

关 键 词：概率级联布尔网络 镇定 矩阵半张量积 随机演化布尔博弈 

分 类 号：O157.5[理学—数学] O151.21[理学—基础数学]