Complete synchronisation for two coupled logical systems

Abstract

This brief article studies the complete synchronisation of two logical systems coupled in the drive-response configuration, where the drive system is a Boolean network (BN), and the response system is a switched BN. Necessary and sufficient conditions are given when the transition matrix of the drive system is invertible, semi-convergent or neither is.Finally, examples are worked out to illustrate the proposed results.

Synchronisation analysis of Boolean networks based on equivalence

“…On the basis of the STP, the issue concerning complete synchronisation of two deterministic BNs has been studied in [23], and some necessary and sufficient algebraic criterions for complete synchronisation have been presented. Later, the results have been further extended in a series of recent works [24][25][26][27][28]. In the recent paper [29], the concept of partial synchronisation has been introduced for two coupled k-valued logical networks with n nodes, respectively (when k = 2, it degenerates into the drive-response BNs), and a necessary and sufficient algebraic criterion for general synchronisation has been obtained based on the approach developed in [23].…”