Fast-Time Stability of Temporal Boolean Networks

In real systems, most of the biological functionalities come from the fact that the connections are not active all the time. Based on the fact, temporal Boolean networks (TBNs) are proposed in this paper, and the fast-time stability is analyzed via semi-tensor product (STP) of matrices and incidence...

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Vydané v:IEEE transaction on neural networks and learning systems Ročník 30; číslo 8; s. 2285 - 2294
Hlavní autori: Li, Bowen, Lu, Jianquan, Zhong, Jie, Liu, Yang
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States IEEE 01.08.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Biological information theory
Boolean algebra
Boolean functions
Computational complexity
Computer applications
Controllability
Fast-time stability
Incidence
incidence matrices
Mathematical analysis
Nodes
pinning control
Polynomials
semi-tensor product (STP)
Stability analysis
Stability criteria
temporal Boolean network (TBN)
Tensors
Trajectory
ISSN:2162-237X, 2162-2388, 2162-2388
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Shrnutí:In real systems, most of the biological functionalities come from the fact that the connections are not active all the time. Based on the fact, temporal Boolean networks (TBNs) are proposed in this paper, and the fast-time stability is analyzed via semi-tensor product (STP) of matrices and incidence matrices. First, the algebraic form of a TBN is obtained based on the STP method, and one necessary and sufficient condition for global fast-time stability is presented. Moreover, incidence matrices are used to obtain several sufficient conditions, which reduce the computational complexity from <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(n2^{n}) </tex-math></inline-formula> (exponential type) to <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(n^{4}) </tex-math></inline-formula> (polynomial type) compared with the STP method. In addition, the global fast-time stabilization of TBNs is considered, and pinning controllers are designed based on the neighbors of controlled nodes rather than all the nodes. Finally, the local fast-time stability of TBNs is considered based on the incidence matrices as well. Several examples are provided to illustrate the effectiveness of the obtained results.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2018.2881459