Synchronization and stability for asynchronous temporal Boolean networks

Lunshi Xu (), Hao Zhang, Jianquan Lu (), Chuan Zhang (), Xianghui Su () and Sultan M. Alghamdi
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Lunshi Xu: College of Computer Science and Technology (Big Data), Taiyuan University of Technology, Jinzhong, Shanxi, P. R. China
Hao Zhang: College of Computer Science and Technology (Big Data), Taiyuan University of Technology, Jinzhong, Shanxi, P. R. China
Jianquan Lu: ��School of Mathematics, Southeast University, Nanjing, Jiangsu, P. R. China
Chuan Zhang: ��School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, P. R. China
Xianghui Su: College of Computer Science and Technology (Big Data), Taiyuan University of Technology, Jinzhong, Shanxi, P. R. China
Sultan M. Alghamdi: �Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 03, 1-17

Abstract: Asynchronous temporal Boolean Networks (ATBNs) are more complex in structure and have different linear expressions compared to traditional synchronous Boolean networks. The complexity depends on the number of updated nodes. The main contribution of this paper is to propose results of synchronization and anti-synchronization problems of ATBNs. First, this paper abstracts two Temporal Boolean Networks (TBNs) into a mathematical model, and provides a linear expression of the network by means of the semi-tensor product (STP) tool. Second, based on the asynchronous updating scheme of temporal Boolean networks, we investigate the synchronization (including complete synchronization and anti-synchronization) of ATBNs, and provide two results to guarantee the synchronization and anti-synchronization. Finally, we provide two examples to verify the correctness of our theorems and corollaries.

Keywords: Semi-tensor product (STP); asynchronous temporal Boolean network (ATBN); synchronization; anti-synchronization (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501997

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