The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
A Linear Representation of Dynamics of Boolean Networks
Abstract
A new matrix product, called semi-tensor product of matrices, is reviewed. Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping. Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system. Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor. The corresponding algorithms are developed and used to some examples.
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Cites
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Metabolic stability and epigenesis in randomly constructed genetic nets
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A N EW A PPROACH TO D ECODING L IFE : Systems Biology
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Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks
Shmulevich, I., Dougherty, E. R., Kim, S., & Zhang, W. (2002) · Bioinformatics · doi:10.1093/bioinformatics/18.2.261 · Cited by 1,608
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Controllability and observability of Boolean control networks
Cheng, D., & Qi, H. (2009) · Automatica · doi:10.1016/j.automatica.2009.03.006 · Cited by 770
Self-citationHuang, S., & Ingber, D. E. (2000) · Experimental Cell Research · doi:10.1006/excr.2000.5044 · Cited by 606
Cited by
Controllability and observability of Boolean control networks
Cheng, D., & Qi, H. (2009) · Automatica · doi:10.1016/j.automatica.2009.03.006 · Cited by 770
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Metadata
- Authors
- Cheng, D., & Qi, H.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2010-10
- Volume
- 55
- Issue
- 10
- Pages
- 2251-2258
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2136433622
- Cited by
- 697
- References
- 32
- FWCI
- 12.05
- Type
- journal article
- Language
- en
- Open access
- closed
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