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. 2020 Jul 14;8:809. doi: 10.3389/fbioe.2020.00809

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Copyright © 2020 Han, Zhong, Hu, Liu, Liu and Ling.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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The application of SNE method in numerical simulation. (A) The numerical simulation is based on a model of a 16-node regulatory network. (B) The curve of SNE score H defined in Eq. (3) suddenly increases when the system is near the critical point (p = 0), which is viewed as a state transition at a bifurcation point. (C) The graph shows the dynamical changes of local SNE score defined as in Eq. (2) respectively, for 16 local networks. It can be seen that those local networks centered in the DNB members drastically increase when the system is near the critical point at p = 0, which provides the early warning signals of the imminent critical transition.