具有切换概率分布的概率布尔网络的依分布稳定和镇定

Stability and stabilization in distribution of probabilistic boolean networks with switching probability distribution

中文关键词  概率布尔网络  切换概率分布  稳定  镇定  矩阵半张量积

英文关键词  Probabilistic Boolean network  Switching probability distribution  Stability  Stabilization  Semi-tensor product of matrices

中文摘要

      布尔网络作为研究基因调控网络的一种重要模型, 近年来引起了国内外很多学者的广泛关注. 本文利用代数状态空间表示方法, 研究具有切换概率分布的概率布尔网络的依分布稳定和镇定问题. 首先, 回顾针对切换布尔网络稳定性分析的现有的研究结果. 其次, 给出具有切换概率分布的概率布尔网络依分布稳定的定义, 并利用矩阵的半张量积建立具有切换概率分布的概率布尔网络的代数表示. 再次, 基于该代数表示, 建立具有切换概率分布的概率布尔网络的依分布稳定的充分必要条件. 最后, 给出具有切换概率分布的概率布尔控制网络镇定问题可解的充要条件, 并给出相应的控制设计方法.

英文摘要

      As an important model for studying gene regulatory networks, Boolean networks have attracted extensive attention from many scholars in the past few decades. Using the algebraic state space representation method, this paper investigates the stability and stabilization in distribution of probabilistic Boolean networks (PBNs) with switching probability distribution (SPD). Firstly, the existing results on the stability of switched Boolean networks are briefly reviewed. Secondly, the definition of stability in distribution of PBNs with SPD is given, and based on the semi-tensor product of the matrices, PBNs with SPD can be converted into the algebraic representation. Thirdly, based on the algebraic representation, a necessary and sufficient condition is presented for the stability in distribution of PBNs with SPD. Finally, a necessary and sufficient condition is presented for the stabilization in distribution of PBNs with SPD, and the corresponding control design method is given.