Long-Run Behavior Estimation of Temporal Boolean Networks With Multiple Data Losses

This brief devotes to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, based on which an augmented system is constructed to facilitate the analysis. A theorem guarantees that the asymptotical stability of the original system can be converted to that of the augmented system. Subsequently, one necessary and sufficient condition is obtained for asymptotical stability. Furthermore, an auxiliary system is derived to study the synchronization issue of the ideal TBNs with normal data transmission and TBNs with multiple data losses, as well as an effective criterion for verifying synchronization. Finally, numerical examples are given to illustrate the validity of the theoretical results.

Automated summary

This study is dedicated to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, and an augmented system is constructed for analysis. A theorem shows that the asymptotical stability of the original system can be converted to that of the augmented system. A necessary and sufficient condition for asymptotical stability is obtained. Additionally, an auxiliary system is derived to study the synchronization issue of ideal TBNs and TBNs with multiple data losses, along with an effective criterion for verifying synchronization. Numerical examples are provided to demonstrate the validity of the theoretical results.