title: Predicting the Lifetime of Dynamic Networks Experiencing Persistent Random Attacks.
abstract: 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.
authors.affiliation: University of Rijeka, Faculty of Civil Engineering, Rijeka, 51000, Croatia.|Boston University, Center for Polymer Studies, Department of Physics, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.|Zagreb School of Economics and Management, Zagreb, 10000, Croatia.|University of Ljubljana, Faculty of Economics, Ljubljana, 1000, Slovenia.
authors.forename: Boris
authors.initials: B
authors.lastname: Podobnik
authors.affiliation: Boston University, Center for Polymer Studies, Department of Physics, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.|Rudjer Boskovic Institute, Centre for Informatics and Computing, Zagreb, 10000, Croatia.
authors.forename: Tomislav
authors.initials: T
authors.lastname: Lipic
authors.affiliation: University of Zagreb, Physics Department, Zagreb, 10000, Croatia.
authors.forename: Davor
authors.initials: D
authors.lastname: Horvatic
authors.affiliation: Boston University, Center for Polymer Studies, Department of Physics, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.
authors.forename: Antonio
authors.initials: A
authors.lastname: Majdandzic
authors.affiliation: University College London, Department of Mathematics, Gower Street, London, WC1E 6BT, UK.
authors.forename: Steven R
authors.initials: SR
authors.lastname: Bishop
authors.affiliation: Boston University, Center for Polymer Studies, Department of Physics, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.
authors.forename: H
authors.initials: H
authors.lastname: Eugene Stanley
mesh_terms: D016494:Computer Security; D007255:Information Services; D008962:Models, Theoretical