Asymptotic Stability of Boolean Networks With Multiple Missing Data
Chi Huang, Wei Wang, Jianquan Lu, Jürgen Kurths
Abstract
In actual network transmission, data loss due to network congestion and power shortage is unavoidable. However, this phenomenon has not been considered in Boolean networks (BNs) analysis so far. The loss of data is usually random, so BNs with missing data are modeled by introducing Bernoulli distribution sequences. A novel augmented system is constructed to deal with the randomly missing data. The initial states of the BNs are supposed to be chosen from the whole space or only part of it, which leads to the global and local stable problems. Some necessary and sufficient conditions are proposed for both problems. Two algorithms are developed to check the asymptotic stability of BNs. An illustrative example is also given to show the effectiveness of the derived results.