Diversified dynamic effects and their order origins in Boolean functions.

Interaction relationships are fundamental to the behavior of complex systems. This study, grounded in Boolean discrete systems, conducts a comprehensive investigation of ordered Boolean functions, elucidating their stabilization capacities, sources of ordering, and significance in gene networks. Our findings confirm that, irrespective of their original configuration or mode, ordered Boolean functions enhance system stability and pattern formation in diverse manners, rescuing systems from chaotic states. This enhancement in stability is evident and intricately connected to mapping tables of functions, reflected through diverse order metrics such as sensitivity, effective edge, and intrinsic order. An analysis of current gene network data reveals that the prevalence of ordered Boolean functions is tightly associated with gene regulation modes. The prominence of canalized and threshold functions signifies distinct genetic regulation behaviors, whereas the abundance of clique functions suggests unexplored mechanisms underlying gene regulation. • Ordered Boolean functions (OBFs) can enhance system stability in diverse manners. • Sensitivity and effective connection of OBFs are approximately equivalent. • The inherent orderliness of OBFs exhibits noticeable discrepancy. • Canalized and threshold modes are ubiquitous in gene regulatory networks. [ABSTRACT FROM AUTHOR]