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Algebraic Representation of Asynchronous Multiple-Valued Networks and Its Dynamics
July-Aug. 2013 (vol. 10 no. 4)
pp. 927-938
Chao Luo, Fac. of Electron. Inf. & Electr. Eng., Dalian Univ. of Technol., Dalian, China
Xingyuan Wang, Fac. of Electron. Inf. & Electr. Eng., Dalian Univ. of Technol., Dalian, China
In this paper, dynamics of asynchronous multiple-valued networks (AMVNs) are investigated based on linear representation. By semitensor product of matrices, we convert AMVNs into the discrete-time linear representation. A general formula to calculate all of network transition matrices of a specific AMVN is achieved. A necessary and sufficient algebraic criterion to determine whether a given state belongs to loose attractors of length s is proposed. Formulas for the numbers of attractors in AMVNs are provided. Finally, algorithms are presented to detect all of the attractors and basins. Examples are shown to demonstrate the feasibility of the proposed scheme.
Index Terms:
network theory (graphs),genetics,matrix algebra,attractors,algebraic representation,asynchronous multiple-valued network dynamics,semitensor product,AMVN,discrete-time linear representation,network transition matrices,loose attractors,basins,Vectors,Computational biology,Bioinformatics,Biological system modeling,Heuristic algorithms,Data structures,Boolean functions,dynamics,Multiple-valued networks,asynchronous stochastic update,algebraic representation
Citation:
Chao Luo, Xingyuan Wang, "Algebraic Representation of Asynchronous Multiple-Valued Networks and Its Dynamics," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 927-938, July-Aug. 2013, doi:10.1109/TCBB.2013.112
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