收稿日期: 2010-08-03
修回日期: 2010-09-27
网络出版日期: 2011-07-15
基金资助
Supported by National Natural Science Foundation of China(60674022, 60736022, 60821091)
Structure of higher order Boolean networks
Received date: 2010-08-03
Revised date: 2010-09-27
Online published: 2011-07-15
Supported by
Supported by National Natural Science Foundation of China(60674022, 60736022, 60821091)
李志强 , 赵寅 , 程代展 . 高阶布尔网络的结构[J]. 中国科学院大学学报, 2011 , 28(4) : 431 -447 . DOI: 10.7523/j.issn.2095-6134.2011.4.003
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
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