Phase transition of Boolean networks with partially nested canalizing functions
Phase transition of Boolean networks with partially nested canalizing functions
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DOI：
10.1140/epjb/e2013-40009-4
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发表时间：
2013-07-01
影响因子：
1.6
通讯作者：
Matache, Mihaela Teodora
中科院分区：
文献类型：
--
作者：
Jansen, Kayse;Matache, Mihaela Teodora
我们生成的临界条件的布尔网络的相变所管辖的部分嵌套的管道化功能的一小部分的输入是管道化，而其余的非管道化的输入服从一个互补的阈值布尔函数。过去的研究已经考虑了完全或部分嵌套渠化函数与互补函数的随机选择配对的稳定性。在其中一些研究中，关于混沌行为的存在，发现了相互矛盾的结果。此外，这些研究主要集中在遍历网络中的初始状态被假定为同样可能。我们放松了这一假设，找到了非遍历情形下网络灵敏度的临界条件。我们使用所提出的数学模型来确定从有序到混沌的相变发生的参数值。我们生成德里达图，以表明数学模型与实际网络动态相匹配。相变图表明，秩序和混乱都可以发生，某些参数诱导一个更大的范围内的值导致秩序与混乱。混沌曲线的边缘确定解析和数值。它示出，渠化的深度不会导致重大的动态变化，一旦达到一定的阈值，这些阈值是相当小的节点的连接性相比。
We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the critical condition for the sensitivity of the network under a non-ergodic scenario. We use the proposed mathematical model to determine parameter values for which phase transitions from order to chaos occur. We generate Derrida plots to show that the mathematical model matches the actual network dynamics. The phase transition diagrams indicate that both order and chaos can occur, and that certain parameters induce a larger range of values leading to order versus chaos. The edge-of-chaos curves are identified analytically and numerically. It is shown that the depth of canalization does not cause major dynamical changes once certain thresholds are reached; these thresholds are fairly small in comparison to the connectivity of the nodes.