A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network. (English) Zbl 1338.94003
Summary: To describe failure propagation dynamics in complex dynamical communication networks, we propose an efficient and compartmental standard-exception-failure propagation dynamics model based on the method of modeling disease propagation in social networks. Mathematical formulas are derived and differential equations are solved to analyze the equilibrium of the propagation dynamics. Stability is evaluated in terms of the balance factor \(G\) and it is shown that equilibrium where the number of nodes in different states does not change, is globally asymptotically stable if \(G\geq 1\). The theoretical results derived are verified by numerical simulations. We also investigate the effect of some network parameters, e.g. node density and node movement speed, on the failure propagation dynamics in complex dynamical communication networks to gain insights for effective measures of control of the scale and duration of the failure propagation in complex dynamical communication networks.
Keywords:
dynamics model; fault propagation; equilibrium analysis; standard-exception-failure propagation model; complex dynamical communication networkReferences:
| [1] | Wang, X. F.; Chen, G., Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 49, 1, 54-62 (2002) · Zbl 1368.93576 |
| [2] | Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D., Complex networks: structure and dynamics, Phys. Rep., 424, 4, 175-308 (2006) · Zbl 1371.82002 |
| [3] | Piqueira, J. R.C.; Araujo, V. O., A modified epidemiological model for computer viruses, Appl. Math. Comput., 213, 2, 355-360 (2009) · Zbl 1185.68133 |
| [4] | Dobson, Ian; Carreras, Benjamin A.; Lynch, Vickie E.; Newman, David E., Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization, Chaos Interdiscip. J. Nonlinear Sci., 17, 2, 026103 (2007) · Zbl 1159.37344 |
| [5] | Lee, T. H.; Park, J. H.; Jung, H. Y., Synchronization of a delayed complex dynamical network with free coupling matrix, Nonlinear Dyn., 69, 3, 1081-1090 (2012) · Zbl 1253.93066 |
| [6] | Gaonkar, R. S.; Viswanadham, N., Analytical framework for the management of risk in supply chains, IEEE Trans. Autom. Sci. Eng., 4, 2, 265-273 (2007) |
| [7] | Ji, D. H.; Jeong, S. C.; Park, Ju H.; Lee, S. M.; Won, S. C., Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Appl. Math. Comput., 218, 9, 4872-4880 (2012) · Zbl 1238.93053 |
| [8] | Moreno, Y.; Pastor-Satorras, R.; Vázquez, A., Critical load and congestion instabilities in scale-free networks, Europhys. Lett., 62, 2, 292 (2003) |
| [9] | Lee, D. S.; Goh, K. I.; Kahng, B.; Kim, D., Sandpile avalanche dynamics on scale-free networks, Physica A, 338, 1, 84-91 (2004) |
| [10] | Moreno, Y.; Pastor-Satorras, R.; Vázquez, A.; Vespignani, A., Critical load and congestion instabilities in scale-free networks, Europhys. Lett., 62, 2, 292 (2007) |
| [11] | Ma, X. J.; Ma, F. X.; Zhao, H. X., Cascading failure in coupled map lattices with directed network, J. Comput. Appl., 7, 063 (2011) |
| [12] | Dou, B. L.; Zhang, S. Y., Load-capacity model for cascading failures of complex networks, J. Syst. Simul., 23, 7, 1459 (2011) |
| [13] | Cavalcante, A. B.; Grajzer, M., Fault propagation model for ad hoc networks, IEEE Int. Conf. Commun., 1-5 (2011) |
| [16] | Mishra, B. K.; Saini, D. K., SEIRS epidemic model with delay for transmission of malicious objects in computer network, Appl. Math. Comput., 188, 2, 1476-1482 (2007) · Zbl 1118.68014 |
| [17] | Yuan, H.; Chen, G., Network virus-epidemic model with the point-to-group information propagation, Appl. Math. Comput., 206, 1, 357-367 (2008) · Zbl 1162.68404 |
| [18] | Meng, X.; Chen, L., The dynamics of a new SIR epidemic model concerning pulse vaccination strategy, Appl. Math. Comput., 197, 2, 582-597 (2008) · Zbl 1131.92056 |
| [19] | Mishra, B. K.; Jha, N., SEIQRS model for the transmission of malicious objects in computer network, Appl. Math Modell., 34, 3, 710-715 (2010) · Zbl 1185.68042 |
| [20] | Mishra, B. K.; Pandey, S. K., Dynamic model of worms with vertical transmission in computer network, Appl. Math. Comput., 217, 21, 8438-8446 (2011) · Zbl 1219.68080 |
| [21] | Song, L. P.; Jin, Z.; Sun, G. Q.; Zhang, J.; Han, X., Influence of removable devices on computer worms: dynamic analysis and control strategies, Comput. Math. Appl., 61, 7, 1823-1829 (2011) · Zbl 1219.37065 |
| [22] | Yang, Lu-Xing; Yang, Xiaofan; Wen, Luosheng; Liu, Jiming, A novel computer virus propagation model and its dynamics, Int. J. Comput. Math., 89, 17, 2307-2314 (2010) · Zbl 1255.68058 |
| [23] | Zio, E.; Sansavini, G., Component criticality in failure cascade processes of network systems, Risk Anal., 31, 8, 1196-1210 (2011) |
| [24] | Mishra, B. K.; Pandey, S. K., Dynamic model of worm propagation in computer network, Appl. Math. Modell. (2013) |
| [25] | Gan, Chenquan; Yang, Xiaofan; Liu, Wanping; Zhu, Qingyi, A propagation model of computer virus with nonlinear vaccination probability, Commun. Nonlinear Sci. Numer. Simul., 19, 1, 92-100 (2014) |
| [26] | Buscarino, A.; Fortuna, L.; Frasca, M.; Latora, V., Disease spreading in populations of moving agents, Europhys. Lett., 82, 3, 38002 (2008) |
| [27] | Yang, Han-Xin; Wang, Wen-Xu; Xie, Yan-Bo; Lai, Ying-Cheng; Wang, Bing-Hong, Transportation dynamics on networks of mobile agents, Phys. Rev. E, 83, 1, 016102 (2011) |
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.
