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Solvable non-Markovian dynamic network

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posted on 2023-06-08, 23:53 authored by Nicos GeorgiouNicos Georgiou, Istvan Kiss, Enrico Scalas
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E

ISSN

1539-3755

Publisher

American Physical Society

Issue

4

Volume

92

Page range

042801

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-01-07

First Open Access (FOA) Date

2016-12-07

First Compliant Deposit (FCD) Date

2016-01-06

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