切换奇异布尔网络的稳定性分析

基因调控网络的稳定性分析是系统生物学的研究热点问题之一.本文利用矩阵半张量积方法研究了切换奇异布尔网络的稳定性问题.首先给出了切换奇异布尔网络的代数表示,基于该代数表示,建立了系统解存在唯一的充要条件.然后通过将切换奇异布尔网络转化为等价的切换布尔网络,分别得到了系统在任意切换下稳定以及切换可稳的充要条件.最后给出例子验证所得结果的有效性.

Stability analysis for switched singular Boolean networks

The stability analysis of gene regulatory networks is a hot topic in systems biology. We investigate the stability of switched singular Boolean networks (SSBNs) by using the semi-tensor product of matrices. First, the dynamics of SSBNs is converted to an algebraic form, based on which a necessary and sufficient condition is established for the uniqueness of solution of SSBNs. Second, several necessary and sufficient conditions are presented for the stability of SSBNs under arbitrary switching signal and the switching stabilizability of SSBNs, respectively, by converting an SSBN into an equivalent switched Boolean network. Two illustrative examples are presented to show that the main results obtained in this paper are effective in analyzing the stability of SSBNs.