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Solvable non-Markovian dynamic network.

Nicos Georgiou1, Istvan Z Kiss1, Enrico Scalas1

  • 1School of Mathematics and Physical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom.

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|November 14, 2015
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Summary
This summary is machine-generated.

This study models complex non-Markovian dynamic networks using a Mittag-Leffler distribution. The developed analytical model accurately approximates network dynamics with power-law interevent times, crucial for understanding real-world systems.

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Area of Science:

  • Complex Systems Science
  • Network Dynamics
  • Stochastic Processes

Background:

  • Non-Markovian processes are prevalent but challenging to model explicitly.
  • Existing models often struggle with heavy-tailed interevent times common in real-world systems.
  • Dynamic networks with random link changes require advanced analytical tools.

Purpose of the Study:

  • To develop an analytically tractable model for non-Markovian dynamic networks.
  • To investigate the use of the Mittag-Leffler distribution for interevent times.
  • To approximate network dynamics characterized by power-law interevent times.

Main Methods:

  • Derivation of Kolmogorov-like forward equations using the Caputo derivative.
  • Analytical and computational solution for the probability of active links.
  • Simulations of random link activation and deletion (RLAD) with power-law interevent times.

Main Results:

  • An analytically solvable Mittag-Leffler model was derived for network link dynamics.
  • Excellent agreement was shown between the Mittag-Leffler model and RLAD simulations.
  • The model accurately approximated susceptible-infected-susceptible spreading dynamics on these networks.

Conclusions:

  • The Mittag-Leffler distribution provides an effective analytical approximation for non-Markovian network dynamics with power-law interevent times.
  • The derived model offers a computationally tractable approach for analyzing complex systems.
  • This work lays the foundation for further generalizations in modeling non-Markovian systems.