Solvable non-Markovian dynamic network.

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.