TY - JOUR

T1 - Stability and Stabilization in Probability of Probabilistic Boolean Networks

AU - Huang, Chi

AU - Lu, Jianquan

AU - Zhai, Guisheng

AU - Cao, Jinde

AU - Lu, Guoping

AU - Perc, Matjaz

N1 - Funding Information:
Manuscript received February 25, 2019; revised August 12, 2019 and November 28, 2019; accepted February 27, 2020. Date of publication March 24, 2020; date of current version January 5, 2021. This work was supported in part by the National Natural Science Foundation of China under Grant 61603268, Grant 61573102, Grant 61272530, and Grant 61573096, in part by the Fundamental Research Funds for the Central Universities under Grant JBK190502, in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20170019, and in part by Slovenian Research Agency under Grant J4-9302, Grant J1-9112, and Grant P1-0403. (Corresponding author: Chi Huang.) Chi Huang is with the School of Economic Information and Engineering, Southwestern University of Finance and Economics, Chengdu 610074, China, and also with the School of Mathematics, Southeast University, Nanjing 210096, China (e-mail: huangchi@swufe.edu.cn).
Publisher Copyright:
© 2012 IEEE.

PY - 2021/1

Y1 - 2021/1

N2 - This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

AB - This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

KW - Probabilistic Boolean network (PBN)

KW - semitensor product (STP)

KW - stability/stabilization in probability

KW - state feedback control

UR - http://www.scopus.com/inward/record.url?scp=85094162291&partnerID=8YFLogxK

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U2 - 10.1109/TNNLS.2020.2978345

DO - 10.1109/TNNLS.2020.2978345

M3 - Article

C2 - 32217481

AN - SCOPUS:85094162291

VL - 32

SP - 241

EP - 251

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

SN - 2162-237X

IS - 1

M1 - 9046240

ER -