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.

中文翻译：

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布尔函数中的多样化动态效果及其顺序来源


交互关系是复杂系统行为的基础。本研究以布尔离散系统为基础，对有序布尔函数进行了全面调查，阐明了它们的稳定能力、排序来源和基因网络的重要性。我们的研究结果证实，无论它们的原始配置或模式如何，有序布尔函数都以不同的方式增强了系统稳定性和模式形成，将系统从混沌状态中拯救出来。这种稳定性的增强是显而易见的，并且与函数的映射表有着错综复杂的联系，反映在不同的顺序指标上，例如灵敏度、有效边缘和内在顺序。对当前基因网络数据的分析表明，有序布尔函数的普遍性与基因调控模式密切相关。通道化和阈值功能的突出意味着不同的遗传调控行为，而团功能的丰富性表明基因调控的潜在机制尚未被探索。