Structure of higher order Boolean networks

doi:10.7523/j.issn.2095-6134.2011.4.003

›› 2011, Vol. 28 ›› Issue (4): 431-447.DOI: 10.7523/j.issn.2095-6134.2011.4.003

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Structure of higher order Boolean networks

LI Zhi-Qiang¹, ZHAO Yin², CHENG Dai-Zhan²

1. Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450002, China;
2. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciances, Beijing 100190, China

Received:2010-08-03 Revised:2010-09-27 Online:2011-07-15
Supported by:
Supported by National Natural Science Foundation of China(60674022, 60736022, 60821091)

Abstract

Abstract:

The higher order Boolean (control) network is introduced and its topological structure is studied. Using semi-tensor product of matrices, its dynamics is converted into two algebraic forms, which are standard discrete-time dynamic systems. The one-to-one correspondence of the network dynamics and its first algebraic form is proved, and certain topological structures, including fixed points, cycles, and transient time, of higher order Boolean (control) networks are revealed. The relationship between the original system and its second algebraic form is also studied.

Key words: higher order Boolean network, algebraic form, fixed point, cycle, transient period

CLC Number:

O233

LI Zhi-Qiang, ZHAO Yin, CHENG Dai-Zhan. Structure of higher order Boolean networks[J]. , 2011, 28(4): 431-447.

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Structure of higher order Boolean networks

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