Coupled propagation dynamics of different time evolution scales on double-layer networks

doi:10.3969/j.issn.1000-5641.2022.02.006

Abstract

Abstract:

Using double-layer networks, we constructed a coupled propagation model (Noisy Voter - Susceptible-Infected-Recovery) with different time evolution scales. This coupled spreading process can be characterized by numerical analysis method of microscopic Markov chain theory. We verified the accuracy of the proposed numerical analysis method using a large number of Monte Carlo simulation experiments. We found a crossover phenomenon of the phase transition type in the coupled model. Specifically, when the noise in the opinion formation process is relatively small, the information propagation scale and the proportion of positive opinions change discontinuously with the information transmission rate. At the same time, the hysteresis loop and bistability phenomenon appear, in which the phenomenon of global consensus can be observed. When the noise is large, the order parameters of these two dynamic processes vary continuously with the transmission rate.

Key words: double-layer networks, time evolution scales, coupled propagation, phase transition, crossover phenomenon

CLC Number:

TP393

Yingqi ZENG, Min TANG. Coupled propagation dynamics of different time evolution scales on double-layer networks[J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 45-54.

Figures/Tables 5

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References 30

1	NEWMAN M E J. The structure and function of complex networks. SIAM Review, 2003, 45 (2): 167- 256. doi: 10.1137/S003614450342480
2	PASTOR-SATORRAS R, VÁZQUEZ A, VESPIGNANI A. Dynamical and correlation properties of the Internet. Physical Review Letters, 2001, 87 (25): 258701. doi: 10.1103/PhysRevLett.87.258701
3	COHEN R, EREZ K, BEN-AVRAHAM D, et al. Resilience of the Internet to random breakdowns. Physical Review Letters, 2000, 85 (21): 4626- 4268. doi: 10.1103/PhysRevLett.85.4626
4	GALLOS L K, COHEN R, ARGYRAKIS P, et al. Stability and topology of scale-free networks under attack and defense strategies. Physical Review Letters, 2005, 94 (18): 188701. doi: 10.1103/PhysRevLett.94.188701
5	DÖRFLER F, CHERTKOV M, BULLO F. Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences of the United States of America, 2013, 110 (6): 2005- 2010. doi: 10.1073/pnas.1212134110
6	SHAO J, HAVLIN S, STANLEY H E. Dynamic opinion model and invasion percolation. Physical Review Letters, 2009, 103 (1): 018701. doi: 10.1103/PhysRevLett.103.018701
7	PASTOR-SATORRAS R, CASTELLANO C, VAN MIEGHEM P, et al. Epidemic processes in complex networks. Review of Modern Physics, 2015, 87 (3): 120- 131.
8	KURANT M, THIRAN P. Layered complex networks. Physical Review Letters, 2006, 96 (13): 138701. doi: 10.1103/PhysRevLett.96.138701
9	MUCHA P J, RICHARDSON T, MACON K, et al. Community structure in time-dependent, multiscale, and multiplex networks. Science, 2010, 328 (5980): 876- 878. doi: 10.1126/science.1184819
10	SZELL M, LAMBIOTTE R, THURNER S. Multirelational organization of large-scale social networks in an online world. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107 (31): 13636- 13641. doi: 10.1073/pnas.1004008107
11	BAXTER G J, DOROGOVTSEV S N, GOLTSEV A V, et al. Avalanche collapse of interdependent networks. Physical Review Letters, 2012, 109 (24): 248701. doi: 10.1103/PhysRevLett.109.248701
12	CAI W R, CHEN L, GHANBARNEJAD F, et al. Avalanche outbreaks emerging in cooperative contagions. Nature Physics, 2015, (11): 936- 940.
13	SANZ J, XIA C Y, MELONI S, et al. Dynamics of interacting diseases. Physical Review X, 2014, 4 (4): 041005. doi: 10.1103/PhysRevX.4.041005
14	DANZIGER M M, BONAMASSA I, BOCCALETTI S, et al. Dynamic interdependence and competition in multilayer networks. Nature Physics, 2019, 15 (2): 178- 185. doi: 10.1038/s41567-018-0343-1
15	NICOSIA V, SKARDAL P S, ARENAS A, et al. Collective phenomena emerging from the interactions between dynamical processes in multiplex networks. Physical Review Letters, 2017, 118 (13): 138302. doi: 10.1103/PhysRevLett.118.138302
16	SORIANO-PAÑOS D, GUO Q T, LATORA V, et al. Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks. Physical Review E, 2019, 99 (6): 62311.
17	PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks. Physical Review Letters, 2001, 86 (14): 3200- 3203. doi: 10.1103/PhysRevLett.86.3200
18	NISHIKAWA T, MOTTER A E, LAI Y C, et al. Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?[J]. Physical Review Letters, 2003, 91(1): 014101.
19	GOMEZ-GARDENES J, MORENO Y, ARENAS A. Paths to synchronization on complex networks. Physical Review Letters, 2007, 98 (3): 034101. doi: 10.1103/PhysRevLett.98.034101
20	VELÁSQUEZ-ROJAS F, VAZQUEZ F. Interacting opinion and disease dynamics in multiplex networks: Discontinuous phase transition and nonmonotonic consensus times. Physical Review E, 2017, 95 (5): 052315.
21	BRODKA P, MUSIAL K, JANKOWSKI J. Interacting spreading processes in multilayer networks: A systematic review. IEEE Access, 2020, 8 (1): 10316- 10341.
22	BOCCALETTI S, BIANCONI G, CRIADO R, et al. The structure and dynamics of multilayer networks. Physics Reports, 2014, 544 (1): 1- 122. doi: 10.1016/j.physrep.2014.07.001
23	CARRO A, TORAL R, SAN M M. The noisy voter model on complex networks [J]. Scientific Reports, 2016, 6(1): Article number 24775.
24	SOOD V, REDNER S. Voter model on heterogeneous graphs. Physical Review Letters, 2005, 94 (17): 178701. doi: 10.1103/PhysRevLett.94.178701
25	MORENO Y, PASTOR-SATORRAS R, VESPIGNANI A, et al. Epidemic outbreaks in complex heterogeneous networks. The European Physical Journal B: Condensed Matter and Complex Systems, 2001, 26 (4): 521- 529.
26	CHAKRABARTI D, WANG Y, WANG C X, et al. Epidemic thresholds in real networks [J]. ACM Transactions on Information and System Security, 2008, 10(4): Article number 13.
27	GOMEZ S, ARENAS A, BORGE-HOLTHOEFER J, et al. Discrete-time Markov chain approach to contact-based disease spreading in complex networks. Europhysics Letters, 2010, 89 (3): 038009. doi: 10.1209/0295-5075/89/38009
28	ZHANG H F, WU Z X, TANG M, et al. Effects of behavioral response and vaccination policy on epidemic spreading - an approach based on evolutionary-game dynamics [J]. Scientific Reports, 2015(4): Article number 5666.
29	ZHANG H F, SHU P P, WANG Z, et al. Preferential imitation can invalidate targeted subsidy policies on seasonal-influenza diseases. Applied Mathematics and Computation, 2017, 294 (1): 332- 342.
30	BARABASI A L, ALBERT R. Emergence of scaling in random networks. Science, 1999, 286 (5439): 509- 512. doi: 10.1126/science.286.5439.509

层间影响	联合状态
层间影响	$ \left[ + \mathrm{S}\right] $	$ \left[ + \mathrm{R}\right] $	$ \left[-\mathrm{S}\right] $	$ \left[-\mathrm{R}\right] $
A层对B层的影响	$ {\psi }_{i}\left(t\right)=1 + \epsilon $	$ {\psi }_{i}\left(t\right)=1 + \epsilon $	$ {\psi }_{i}\left(t\right)=1-\epsilon $	$ {\psi }_{i}\left(t\right)=1-\epsilon $
B层对A层的影响	$ {\xi }_{i}^{-}\left(t\right)=1 + \epsilon $	$ {\xi }_{i}^{-}\left(t\right)=1-\epsilon $	$ {\xi }_{i}^{ + }\left(t\right)=1-\epsilon $	$ {\xi }_{i}^{ + }\left(t\right)=1 + \epsilon $

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