Comparison of Topological Structures Between Boolean Control Networks and Nominal Boolean Networks

2018 ◽  
Author(s):  
Xingbang Cui ◽  
Jun-e Feng ◽  
Sen Wang ◽  
Yongyuan Yu
Keyword(s):  
Boolean Networks ◽  
Topological Structures ◽  
Control Networks

scholarly journals Robust Invariant Set Analysis of Boolean Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Bowen Li ◽  
Jungang Lou ◽  
Yang Liu ◽  
Zhen Wang
Keyword(s):  
Fixed Point ◽  
Output Feedback ◽  
Invariant Set ◽  
Boolean Networks ◽  
Sufficient Condition ◽  
Lac Operon ◽  
Feedback Controllers ◽  
Control Networks ◽  
E Coli ◽  
Necessary And Sufficient

In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli.

scholarly journals A Note on the Observability of Temporal Boolean Control Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenping Shi ◽  
Bo Wu ◽  
Jing Han
Keyword(s):  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Control Networks ◽  
Linear Dynamic Systems ◽  
Regulatory Interactions ◽  
Boolean Control Network ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Product Of Matrices

Temporal Boolean network is a generalization of the Boolean network model that takes into account the time series nature of the data and tries to incorporate into the model the possible existence of delayed regulatory interactions among genes. This paper investigates the observability problem of temporal Boolean control networks. Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. An example is given to illustrate the effectiveness of the obtained results.

scholarly journals Structural Controllability of Boolean Control Networks under Partial Information

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qinyao Pan ◽  
Jie Zhong ◽  
Shalin Tong ◽  
Bowen Li ◽  
Xiaoxu Liu
Keyword(s):  
Boolean Functions ◽  
Partial Information ◽  
Sufficient Conditions ◽  
Vital Role ◽  
Boolean Networks ◽  
Lactose Operon ◽  
Control Networks ◽  
Structural Controllability ◽  
Necessary And Sufficient ◽  
Theoretical Results

It is worth noting that both nodes’ coupling connections and logical updating functions play a vital role in state evolutions of Boolean networks (BNs). In this paper, a new concept named structural controllability (SC) about Boolean control networks (BCNs) with known partial information on nodes’ connections is studied. Then, by referring to semi-tensor product (STP) techniques, several types of SC are presented according to different issues of Boolean functions. Thereafter, several necessary and sufficient conditions are derived for SC of BCNs. Finally, a biological model of the lactose operon in Escherichia coli is simulated to show the effectiveness of the main theoretical results.

scholarly journals Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2864
Author(s):  
Wen Liu ◽  
Shihua Fu ◽  
Jianli Zhao
Keyword(s):  
Tensor Product ◽  
Design Method ◽  
Boolean Networks ◽  
Control Networks ◽  
State Subset ◽  
Time Optimal ◽  
Set Stabilization ◽  
Optimal Set

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Reachability and Controllability Analysis of Periodic Switched Boolean Control Networks

2014 ◽  
Vol 26 (5) ◽  
pp. 573-579 ◽  
Author(s):  
Zhiqiang Li ◽  
◽  
Jinli Song ◽  
Huimin Xiao
Keyword(s):  
Boolean Networks ◽  
Control Network ◽  
Discrete Time System ◽  
Vector Form ◽  
Time System ◽  
Control Networks ◽  
Boolean Control Network ◽  
Switching Signal ◽  
And Control ◽  
Periodic Switching

The reachability and controllability of switched Boolean (control) network are discussed in this paper. Based on semi-tensor product, using the vector form of Boolean logical variable, the switched Boolean (control) network is expressed as a discrete time system with state and control variables. For the switched Boolean network without control, the stabilization by suitable switching signal is discussed. Also, the controllability of the periodic switching signal is learned, and the conditions for stability and controllability of periodic switched Boolean networks avoiding states setCare obtained.

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