数学与计算机科学 |
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一类具有临时免疫的时滞蠕虫传播模型的Hopf分支 |
张子振, 毕殿杰, 赵涛 |
安徽财经大学 管理科学与工程学院, 安徽 蚌埠 233030 |
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Delay induced Hopf bifurcation in a worm propagation model with partial immunization |
ZHANG Zizhen, BI Dianjie, ZHAO Tao |
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, Anhui Province, China |
[1] MISHRA B K, PANDEY S K. Dynamic model of worms with vertical transmission in computer network[J]. Applied Mathematics and Computation, 2011, 217(21): 8438-8446. [2] ZHANG Z Z, YANG H Z. Stability and Hopf bifurcation in a delayed SEIRS worm model in computer network[J]. Mathematical Problems in Engineering, 2014, Article ID 319174: 1-9. [3] MISHRA B K, KESHRI N. Mathematical model on the transmission of worms in wireless sensor network[J]. Applied Mathematical Modelling, 2013, 37(6): 4103-4111. [4] ZHANG Z Z, SI F S. Dynamics of a delayed SEIRS-V model on the transmission of worms in a wireless sensor network[J]. Advances in Difference Equations, 2014, 295: 1-14. [5] WANG F W, ZHANG Y K, WANG C G, et al. Stability analysis of a SEIQV epidemic model for rapid spreading worms[J]. Computers and Security, 2010, 29(4): 410-418. [6] PELTOMAKI M, OVASKA M, ALAVA M. Worm spreading with immunization: An interplay of spreading and immunity time scales[J]. Physica A: Statistical Mechanics and Its Applications, 2011, 390(3): 4152-4159. [7] SONG L P, HAN X, LIU D M, et al. Adaptive human behavior in a two-worm interaction model[J]. Discrete Dynamics in Nature and Society, 2012, Article ID 828246: 1-13. [8] YAO Y, FENG X, YANG W, et al. Analysis of a delayedinternet worm propagation model with impulsive quarantine strategy[J]. Mathematical Problems in Engineering, 2014, Article ID 369360: 1-18. [9] WANG F W, YANG Y, ZHAO D M, et al. A worm defending model with partial immunization and its stability analysis[J]. Journal of Communications, 2015, 10(4): 276-283. [10] WANG T, HU Z, LIAO F. Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response[J]. Journal of Mathematical Analysis and Applications, 2014, 411(1): 63-74. [11] WANG L S, FENG G H. Global stability and Hopf bifurcation of a predator-prey model with time delay and stage structure[J]. Journal of Applied Mathematics, 2014, Article ID 431671: 1-10. [12] BIANCA C, FERRARA M, GUERRINI L. The Cai model with time delay: existence of periodic solutions and asymptotic analysis[J]. Applied Mathematics & Information Sciences, 2013, 7(1): 21-27. [13] FENG L, LIAO X, LI H, et al. Hopf bifurcation analysis of a delayed viral infection model in computer networks[J]. Mathematical and Computer Modelling, 2012, 56 (7-8): 167- 179. [14] XU C J, HE X F. Stability and bifurcation analysis in a class of two-neuron networks with resonant bilinear terms[J]. Abstract and Applied Analysis, 2011, Article ID 697630: 1-21. [15] LIU J, LI Y M. Hopf bifurcation analysis of a predator-prey system with delays[J]. Journal of Zhejiang University:Science Edition, 2013,40 (6): 618-626. [16] DONG T, LIAO X, LI H. Stability and Hopf bifurcation in a computer virus model with multistate antivirus[J]. Abstract and Applied Analysis, 2012, Article ID 841987: 1-16. [17] ZHANG T L, JIANG H J, TENG Z D. On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model[J]. Neurocomputing, 2009,72(4-6): 1098-1104. [18] HASSARD B D, KAZARINOFF N D, WAN Y H. Theory and Applications of Hopf Bifurcation[M].Cambridge: Cambridge University Press,1981. |
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