Anti-synchronization of two coupled Boolean networks

Synchronization of mutual time-varying delay-coupled temporal Boolean networks

“…Figure 1. Total synchronization error of BNs (21) and (23) with initial states X 0 = (1, 1, 0) and Y 0 = (0, 0, 0).…”

“…Synchronization occurs between two systems, and there is mutual coupling relationship between the two systems. There are some outstanding results on coupling synchronization, such as synchronization of probabilistic BNs with indirect coupling, 20 partial synchronization of interconnected BNs, 21,22 anti-synchronization of the two coupled BNs, 23 synchronization of the two coupled deterministic BNs, 24 synchronization of the switched BNs, 25,26 complete synchronization of the two coupled BNs, 25 synchronization of the two coupled BNs, 27 and robust synchronization of the two Boolean control networks. 28 This research focuses on synchronization of the BNs with delay coupling or without delay coupling.…”

Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control

“…Taking advantage of STP, the logical form of BNs (or BCNs) can be converted to an algebraic representation, which enables algebraic operations to be applied to the investigation of BNs (or BCNs). STP facilitates the exploration of a number of essential and significant properties enjoyed by BNs and BCNs, such as fixed points, cycles, and basin of attractors of BNs (or BCNs) (Cheng et al, 2010b), as well as some control problems, i.e., disturbance decoupling (Liu Y et al, 2017), controllability (Lu et al, 2016;Zhu QX et al, 2019), observability (Cheng and Qi, 2009;Fornasini and Valcher, 2012), optimal control (Zhu QX et al, 2018), output tracking control (Li YY et al, 2019), network synchronization (Li FF and Yu, 2016), and stabilization (Lu et al, 2018b;Li BW et al, 2019;Sun et al, 2020).…”

Robust Invariant Set Analysis of Boolean Networks

“…Based on this, a BN (or BCN) can be converted into the corresponding algebraic form by calculating its unique transition matrix. Therefore, many fundamental and interesting problems have been investigated for BNs and BCNs, such as the controllability [5,6], stabilization [7][8][9][10][11][12][13][14][15], observability [16][17][18][19], disturbance decoupling problem [20] synchronization [21], function perturbations [22], optimal control [23][24][25][26], normalization problem [27], and others. The STP has also been widely applied in games [28,29] and asynchronous sequential machines [30,31].…”