Set stability and synchronization of logical networks with probabilistic time delays. Issue 15 (October 2018)

• Record Type: Journal Article
• Authors: Ding, Xueying; Li, Haitao; Wang, Shuling
• Is Part Of: Journal of the Franklin Institute. Volume 355:Issue 15(2018)
• Page Start: 7735
• Page End: 7748
• Publication Date: 2018-10
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2018.08.009
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: Using the algebraic state space representation (ASSR) method, this paper investigates the set stability and synchronization of Boolean networks with probabilistic time delays (PTDs). Firstly, an equivalent stochastic system is established for the Boolean network with PTDs by using the ASSR method. Secondly, based on the probabilistic state transition matrix of equivalent stochastic system, a necessary and sufficient condition is proposed for the set stability of Boolean networks with PTDs. Thirdly, as an application of set stability, the synchronization of coupled Boolean networks with PTDs is studied, and a necessary and sufficient condition is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.