Predicting the lifetime of dynamic networks experiencing persistent random attacks

This is the peer reviewed version of the following article: A. Inglis, L. Cruz, D.L. Roe, H.E. Stanley, D.L. Rosene, B. Urbanc. 2008. "Automated identification of neurons and their locations." JOURNAL OF MICROSCOPY, Volume 230, Issue 3, pp. 339 - 352, which has been published in final form at https://doi.org/10.1111/j.1365-2818.2008.01992.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.Estimating the critical points at which complex systems abruptly flip from one state to another is one of the remaining challenges in network science. Due to lack of knowledge about the underlying stochastic processes controlling critical transitions, it is widely considered difficult to determine the location of critical points for real-world networks and it is even more difficult to predict the time at which these potentially catastrophic failures occur. We analyse a class of decaying dynamic networks experiencing persistent failures in which the magnitude of the overall failure is quantified by the probability that a potentially permanent internal failure will occur. When the fraction of active neighbours is reduced to a critical threshold, cascading failures can trigger a total network failure. For this class of network we find that the time to network failure, which is equivalent to network lifetime, is inversely dependent upon the magnitude of the failure and logarithmically dependent on the threshold. We analyse how permanent failures affect network robustness using network lifetime as a measure. These findings provide new methodological insight into system dynamics and, in particular, of the dynamic processes of networks. We illustrate the network model by selected examples from biology and social science.We are grateful to Javier Martin Buldu and Jacobo Aguirre for useful comments and discussion. BP work was partially supported by the University of Rijeka. S.R.B acknowledges the financial support of the Engineering and Physical Sciences Research Council under the grant ENFOLDing - Explaining, Modelling, and Forecasting Global Dynamics, reference EP/H02185X/1. The Boston University work was supported by ONR Grant N00014-14-1-0738, DTRA Grant HDTRA1-14-1-0017 and NSF Grant CMMI 1125290. (University of Rijeka; EP/H02185X/1 - Engineering and Physical Sciences Research Council; N00014-14-1-0738 - ONR Grant; HDTRA1-14-1-0017 - DTRA Grant; CMMI 1125290 - NSF)Published versio