Turing instability induced by complex networks in a reaction-diffusion information propagation model. (English) Zbl 07779162
Summary: The dynamics of rumor spreading in the information environment is a valuable way to study information management and public opinion monitoring. In this paper, the spreading of rumors and the behavior of crowd diffusion on network structure are studied by establishing a Suspicious-Infected (\(SI\)) reaction-diffusion model of rumor spreading with Allee effect. Especially, the necessary conditions for Turing pattern to appear in space are studied. Then, Monte Carlo simulation was used to prove the validity of the model. Furthermore, extensive numerical evaluation of the system is carried out under different networks, whose results show that the diffusion coefficient can change the patterns significantly. Then, on the lattice network and the cellular network, the spatial instability will cause the same pattern type, while the density distributions of \(S\) and \(I\) are no longer consistent on WS networks and BA networks. In addition, the change of the network structure and the introduction of the periodicity of diffusion coefficient will make the instability of the original system disappear in space. These works have certain guiding value to the prediction of rumor spreading scope.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
| 90-XX | Operations research, mathematical programming |
Keywords:
complex network; information diffusion; reaction-diffusion system; Turing instability; spatial patternReferences:
| [1] | Daley, D.; Kendall, D., Stochastic rumors, IMA J. Appl. Math., 1, 42-55 (1965) |
| [2] | Maki, D.; Thompson, M., Mathematical Models and Applications, with Emphasis on the Social, Life and Management Sciences (1973), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey |
| [3] | Varshney, D.; Vishwakarma, D. K., A review on rumour prediction and veracity assessment in online social network, Expert Syst. Appl., 168, Article 114208 pp. (2020) |
| [4] | Li, J. R.; Jiang, H. J.; Mei, X. H.; Hu, C.; Zhang, G. L., Dynamical analysis of rumor spreading model in multi-lingual environment and heterogeneous complex networks, Inform. Sciences, 536, 391-408 (2020) · Zbl 1475.91256 |
| [5] | Zhu, L. H.; Guan, G.; Li, Y. M., Nonlinear dynamical analysis and control strategies of a network-based SIS epidemic model with time delay, Appl. Math. Model., 70, 512-531 (2019) · Zbl 1464.92255 |
| [6] | Singha, J., A new analysis for fractional rumor spreading dynamical model in a social network with Mittag-Leffler law, Chaos, 29, Article 013137 pp. (2019) · Zbl 1406.91326 |
| [7] | Zhu, L. H.; Zhou, M. T.; Zhang, Z. D., Dynamical analysis and control strategies of rumor spreading models in both homogeneous and heterogeneous networks, J. Nonlinear Sci., 30, 2545-2576 (2020) · Zbl 1467.34088 |
| [8] | Huo, L. A.; Wang, L.; Song, N. X.; Ma, C. Y.; He, B., Rumor spreading model considering the activity of spreaders in the homogeneous network, Phys. A, 468, 855-865 (2017) · Zbl 1400.91426 |
| [9] | Huo, L. A.; Cheng, Y. Y.; Liu, C.; Ding, F., Dynamic analysis of rumor spreading model for considering active network nodes and nonlinear spreading rate, Phys. A, 506, 24-35 (2018) · Zbl 1514.91142 |
| [10] | Ma, J.; Zhu, H., Rumor diffusion in heterogeneous networks by considering the individuals’ subjective judgment and diverse characteristics, Phys. A, 499, 276-287 (2018) · Zbl 1514.91127 |
| [11] | Zhu, L. H.; Zhao, H. Y.; Wang, H. Y., Partial differential equation modeling of rumor propagation in complex networks with higher order of organization, Chaos, 29, Article 053106 pp. (2019) · Zbl 1415.91245 |
| [12] | Zanette, D. H., Dynamics of rumor propagation on small-world networks, Phys. Rev. E, 65, Article 041908 pp. (2002) |
| [13] | Iribarren, J. L.; Moro, E., Impact of human activity patters on the dynamics of information diffusion, Phys. Rev. Lett., 103, Article 038702 pp. (2009) |
| [14] | Benson, A. R.; Gleich, D. F.; Leskovec, J., Higher-order organization of complex networks, Science, 353, 163-166 (2016) |
| [15] | Xian, J. J.; Yang, D.; Pan, L. M.; Wang, W.; Wang, Z., Misinformation spreading on correlated multiplex networks, Chaos, 29, Article 113123 pp. (2019) · Zbl 1427.91211 |
| [16] | Moreno, Y.; Nekovee, M.; Pacheco, A. F., Dynamics of rumor spreading in complex networks, Phys. Rev. E, 69, Article 066130 pp. (2004) |
| [17] | Duan, M. R.; Chang, L. L.; Jin, Z., Turing patterns of an SI epidemic model with cross-diffusion on complex networks, Phys. A, 533, Article 122023 pp. (2019) · Zbl 07570026 |
| [18] | Chang, L. L.; Duan, M. R.; Sun, G. Q.; Jin, Z., Cross-diffusion-induced patterns in an SIR epidemic model on complex networks, Chaos, 30, Article 013147 pp. (2020) · Zbl 1431.92113 |
| [19] | Chang, L. L.; Liu, C.; Sun, G. Q.; Wang, Z.; Jin, Z., Delay-induced patterns in a predator-prey model on complex networks with diffusion, New J. Phys., 21, Article 073035 pp. (2019) |
| [20] | Tian, C. R.; Ling, Z.; Zhang, L., Delay-driven spatial patterns in a network-organized semiarid vegetation model, Appl. Math. Comput., 367, Article 124778 pp. (2018) · Zbl 1433.35432 |
| [21] | Tian, C. R.; Ruan, S. G., Pattern formation and synchronism in an allelopathic plankton model with delay in a network, SIAM J. Appl. Dyn. Syst., 18, 531-557 (2019) · Zbl 1416.34071 |
| [22] | Turing, A. M., The chemical basis of morphogenesis, B. Math. Biol, 52, 153-197 (1990) |
| [23] | Hasslacher, B.; Kapral, R.; Lawniczak, A., Molecular Turing structures in the biochemistry of the cell, Chaos, 3, 7-13 (1993) |
| [24] | Chung, J. M.; Peacock-Lópeza, E., Bifurcation diagrams and Turing patterns in a chemical self-replicating reaction-diffusion system with cross diffusion, J. Chem. Phys., 127, Article 174903 pp. (2007) |
| [25] | Li, Q. S.; Ji, L., Control of Turing pattern by weak spatial perturbation, J. Chem. Phys., 120, 9690 (2004) |
| [26] | Mao, Z. G.; Yin, Z. Q.; Ran, J. X., Generation of high-power-density atmospheric pressure plasma with liquid electrodes, Appl. Phys. Lett., 84, 5142 (2004) |
| [27] | Liu, B.; Wu, R. C.; Chen, L. P., Turing-Hopf bifurcation analysis in a superdiffusive predator-prey model, Chaos, 28, Article 113118 pp. (2018) · Zbl 1403.92255 |
| [28] | Ghorai, S. T.; Poria, S., Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity, Chaos, Solitons Fract., 91, 421-429 (2016) · Zbl 1372.92078 |
| [29] | Li, X. X.; Cai, Y. L.; Wang, K.; Fu, S. M.; Wang, W. M., Non-constant positive steady states of a host-parasite model with frequency- and density-dependent transmissions, J. Frankl. Inst., 357, 4392-4413 (2020) · Zbl 1437.92126 |
| [30] | Tiana, C., Delay-driven spatial patterns in a plankton allelopathic system, Chaos, 22, Article 013129 pp. (2012) · Zbl 1331.92150 |
| [31] | Wang, H. J.; Ren, Z., Competition of apatial and temporal instabilities under time delay near codimension-two Turing-Hopf bifurcations, Commun. Theor. Phys., 56, 339 (2011) · Zbl 1247.35061 |
| [32] | Djouda, B. S.; Kakmeni, F. M.; Ghomsi, P., Theoretical analysis of spatial nonhomogeneous patterns of entomopathogenic fungi growth on insect pest, Chaos, 29, Article 053134 pp. (2019) · Zbl 1415.92203 |
| [33] | Liu, Y.; Ruan, S. G.; Yang, L., Stability transition of persistence and extinction in an avian influenza model with Allee effect and stochasticity, Commun. Nonlinear Sci. Numer. Simul., 91, Article 105416 pp. (2020) · Zbl 1460.92210 |
| [34] | Kramer, A. M.; Dennis, B.; Liebhold, A. M.; Drake, J. M., The evidence for Allee effects, Popul. Ecol., 51, 341-354 (2009) |
| [35] | Peng, M.; Zhang, Z. D.; Lim, C. W.; Wang, X. D., Hopf bifurcation and hybrid control of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response, Math. Probl. Eng., 3, 1-12 (2018) · Zbl 1427.37069 |
| [36] | Peng, M.; Zhang, Z. D., Bifurcation analysis and control of a delayed stage-structured predator-prey model with ratio-dependent Holling type III functional response, J. Vib. Control, 26, 1232-1245 (2019) |
| [37] | Li, Y. M.; Sun, Y. Y.; Hua, J.; Li, L., Indirect adaptive type-2 fuzzy impulsive control of nonlinear systems, IEEE Trans. Fuzzy Syst., 23, 1084-1099 (2015) |
| [38] | Dong, G. G.; Qing, T.; Du, R. J.; Wang, C.; Li, R. Q.; Wang, M. G.; Tian, L. X.; Chen, L.; Vilela, A.; Stanle, H., Complex network approach for the structural optimization of global crude oil trade system, J. Clean. Prod., 251, Article 119366 pp. (2020) |
| [39] | Zhang, F. X.; Li, Y. M.; Hua, J., Direct adaptive fuzzy control of SISO nonlinear systems with input-output nonlinear relationship, Int. J. Fuzzy Syst., 20, 1069-1078 (2018) |
| [40] | Brigatti, E.; Oliva, M.; Nunez-Lopez, M.; Oliveros-Ramos, R.; Benavides, J., Pattern formation in a predator-prey system characterized by a spatial scale of interaction, Europhys. Lett., 88, 68002 (2009) |
| [41] | Zhu, L. H.; Liu, W. S.; Zhang, Z. D., Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function, Appl. Math. Comput., 370, Article 124925 pp. (2020) · Zbl 1433.91122 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
