摘要
This study is concerned with probabilistic Boolean control networks(PBCNs)with state feedback control.A novel definition of bisimilar PBCNs is proposed to lower computational complexity.To understand more on bisimulation relations between PBCNs,we resort to a powerful matrix manipulation called semi-tensor product(STP).Because stabilization of networks is of critical importance,the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable.Additionally,the transient periods(the maximum number of steps to implement stabilization)of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation.The results are then extended to the probabilistic Boolean networks.
This study is concerned with probabilistic Boolean control networks(PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs, we resort to a powerful matrix manipulation called semi-tensor product(STP). Because stabilization of networks is of critical importance, the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally, the transient periods(the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.
基金
Project supported by the National Natural Science Foundation of China(Nos.61603268 and 61773319)
the Fundamental Research Funds for the Central Universities,China(No.JBK190502)。
