Solvable non-Markovian dynamic network

Georgiou, Nicos, Kiss, Istvan Z and Scalas, Enrico (2015) Solvable non-Markovian dynamic network. Physical Review E, 92 (4). 042801. ISSN 1539-3755

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Abstract

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 07 Jan 2016 10:46
Last Modified: 29 Jun 2017 11:38
URI: http://sro.sussex.ac.uk/id/eprint/58997

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