Georgiou Nicos, Kiss Istvan Z, Scalas Enrico
School of Mathematics and Physical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042801. doi: 10.1103/PhysRevE.92.042801. Epub 2015 Oct 2.
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.
非马尔可夫过程在自然系统和人造系统中广泛存在，但对此类系统的显式建模和分析仍不够成熟。我们考虑一个具有随机链路激活和删除（RLAD）以及事件间隔时间的重尾米塔格 - 莱夫勒分布的非马尔可夫动态网络。我们利用Caputo导数推导了一个关于网络中具有给定数量活跃链路概率的解析且计算易处理的类柯尔莫哥洛夫前向方程组，并求解它们。还针对幂律事件间隔时间对RLAD进行了模拟研究，结果表明与米塔格 - 莱夫勒模型高度吻合。即使RLAD网络动态与易感 - 感染 - 易感传播动态耦合，这种吻合依然成立。因此，可解析求解的米塔格 - 莱夫勒模型为网络动态以幂律分布的事件间隔时间为特征的情况提供了一个很好的近似。我们进一步讨论了结果可能的推广。
