Recent developments of Boolean networks with switching and constraints

Abstract

A switched Boolean network (SBN) is an important model for describing hybrid phenomena in gene regulatory networks, and it has received increasing attention since the development of the semi-tensor product of matrices. This paper aims to present a comprehensive survey on SBNs. First, the fundamental issues for SBNs with arbitrary switching signals are reviewed, including stability, stabilisation, controllability, observability, optimal control, and synchronisation. Next, a brief review of the stability analysis of SBNs with constrained switching, consisting of time-dependent switching, state-dependent switching, and logical switching, is given. In addition, some basic results on the SBNs under non-ideal conditions are also introduced comprehensively.

Keywords:

• Switched Boolean networks
• gene regulatory networks
• switching signals
• semi-tensor product of matrices

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61973078], [grant number 62073202] and [grant number 62173308, the Natural Science Foundation of Zhejiang Province of China [grant number LR20F030001] and [grant number LD19A010001].

Notes on contributors

Xueying Ding

Xueying Ding received the B.S. and M.S. degrees from the School of Mathematics and Statistics, Shandong Normal University, Jinan, China, in 2016 and 2019, respectively, and the Ph.D. degree at the School of Mathematics, Southeast University, Nanjing, China, in 2023. She is currently an lecturer with the School of Science, Shandong Jianzhu University, Jinan, China. Her research interests include random evolutionary game theory and logical dynamic system.

Jianquan Lu

Jianquan Lu received the B.S. degree in mathematics from Zhejiang Normal University, Zhejiang, China, in 2003, the M.S. degree in mathematics from Southeast University, Nanjing, China, in 2006, and the Ph.D. degree in applied mathematics from City University of Hong Kong, Hong Kong, in 2009. From 2010 to 2012, he was an Alexander von Humboldt Research Fellow in PIK, Germany. He is currently a professor at the Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China. His current research interests include collective behavior in complex dynamical networks and multi-agent systems, logical networks, and hybrid systems.

Haitao Li

Haitao Li received the B.S. and M.S. degrees from the School of Mathematical Science, Shandong Normal University in 2007 and 2010, respectively, and the Ph.D. degree at the School of Control Science and Engineering, Shandong University in 2014. Since 2015, he has been with the School of Mathematics and Statistics, Shandong Normal University, China, where he is currently a professor. From Jan. 2014 to Jan. 2015, he worked as a Research Fellow in Nanyang Technological University, Singapore. His research interests include logical dynamic systems, networked evolutionary games, nonlinear control, etc.

Yang Liu

Yang Liu received the B.S. degree in mathematics from Zhejiang Normal University, Jinhua, China, in 2003, and the Ph.D. degree from Tongji University, Shanghai, China, in 2008.He is currently a Professor with the Department of Mathematics, Zhejiang Normal University. His current research interests include hybrid systems and logical networks.