The Research On Observability Of Boolean Multiplex Networks

Boolean multiplex(multilevel)networks(BMNs)are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis.Studying control-related problems in BMNs may not only provide new views into the intrinsic control in complex biological systems,but also enable us to develop method for manipulating biological systems using exogenous inputs.In this thesis,the observability of the Boolean multiplex networks(BMNs)are studied.First,we give the brief introduction of BMNs.Secondly we introduce the Semi-Tensor Product(STP)approach.We introduce the concepts and properties of STP approach.Then the concepts of observability of Boolean multiplex control networks(BMCNs)are given.We give the necessary and sufficient condition of the observability and proof it.We also make some example to illustrate our results.Finally the dynamical model and structure of probabilistic Boolean multiplex networks are constructed.By using of Semi-Tensor Product(STP)approach,the logical dynamics of probabilistic Boolean multiplex networks is converted into an equivalent algebraic representation.Then,the observability of the probabilistic Boolean multiplex networks is investigated by giving necessary and sufficient conditions.And examples are given to illustrate the efficiency of the obtained theoretical results.