Citation: Meng Zhang, Kaiyuan Liu, Lansun Chen, Zeyu Li. State feedback impulsive control of computer worm and virus with saturated incidence[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1465-1478. doi: 10.3934/mbe.2018067
[1] | [ Y. Cai, Y. Kang and W. Wang, Global stability of the steady states of an epidemic model incorporating intervention strategies, Mathematical Biosciences and Engineering, 14 (2017), 1071-1089. |
[2] | [ L. Chen, X. Liang and Y. Pei, The periodic solutions of the impulsive state feedbck dynamical system, Commun. Math. Biol. Neurosci, 14 (2018). |
[3] | [ A. M. Elaiw, Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynamics, 69 (2012), 423-435. |
[4] | [ A. M. Elaiw, R. M. Abukwaik and E. O. Alzahrani, Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays, International Journal of Biomathematics, 7 (2014), 1450055, 25 pp. |
[5] | [ T. Fukunaga and W. Iwasaki, Inactivity periods and postural change speed can explain atypical postural change patterns of Caenorhabditis elegans mutants, BMC Bioinformatics, 18 (2017), p46. |
[6] | [ H. Guo, L. Chen and X. Song, Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property, Appl. Math. Comput., 271 (2015), 905-922. |
[7] | [ J. D. Hernández Guillén, A. Martín del Rey and L. Hernández Encinas, Study of the stability of a SEIRS model for computer worm propagation, Physica A: Statistical Mechanics and its Applications, 479 (2017), 411-421. |
[8] | [ J. Jia, Z. Jin and L. Chang, Structural calculations and propagation modeling of growing networks based on continuous degree, Mathematical Biosciences and Engineering, 14 (2017), 1215-1232. |
[9] | [ E. Kirmani and C. S. Hood, Analysis of a scanning model of worm propagation, Journal in Computer Virology, 6 (2010), 31-42. |
[10] | [ S. Lefschetz, Contribution to the Theory of Nonlinear Oscillations, Vol. I, Princeton University Press, Princeton, 1950. |
[11] | [ Z. Li, L. Chen and Z. Liu, Periodic solution of a chemostat model with variable yield and impulsive state feedback control, Appl. Math. Model., 36 (2012), 1255-1266. |
[12] | [ X. Liang, Y. Pei and Y. Lv, Modeling the state dependent impulse control for computer virus propagation under media coverage, Physica A: Statistical Mechanics and its Applications, 491 (2018), 516-527. |
[13] | [ B. Liu, Y. Tian and B. Kang, Dynamics on a Holling II predator-prey model with statedependent impulsive control, Int. J. Biomath., 5 (2012), 93-110. |
[14] | [ S. Max, A matter of time: On the transitory nature of cyberweapons, Journal of Strategic Studies, 41 (2018), 6-32. |
[15] | [ G. Pang and L. Chen, Periodic solution of the system with impulsive state feedback control, Nonlinear Dynam., 78 (2014), 743-753. |
[16] | [ D. A. Ray, C. B. Ward and B. Munteanu, etc, Investigating the impact of real-world factors on internet worm propagation, Lecture Notes in Computer Science, 4812 (2007), 10-24. |
[17] | [ M. Sun, Y. Liu and S. Liu, etc, A novel method for analyzing the stability of periodic solution of impulsive state feedback model, Appl. Math. Comput., 273 (2016), 425-434. |
[18] | [ Y. Tian, K. Sun and L. Chen, Modelling and qualitative analysis of a predator-prey system with state-dependent impulsive effects, Math. Comput. Simulat., 82 (2011), 318-331. |
[19] | [ A. Wang, Y. Xiao and H. Zhu, Dynamics of a filippov epidemic model with limited hospital beds, Mathematical Biosciences and Engineering, 15 (2018), 739-764. |
[20] | [ C. Wei and L. Chen, Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control, Journal of Applied Mathematics, 2012 (2012), Art. ID 607105, 17 pp. |
[21] | [ C. Wei and L. Chen, Homoclinic bifurcation of prey-predator model with impulsive state feedback control, Appl. Math. Comput., 237 (2014), 282-292. |
[22] | [ X. Xiao, P. Fu and G. Hu, etc, SAIDR: A new dynamic model for SMS-based worm propagation in mobile networks, IEEE Access, 5 (2017), 9935-9943. |
[23] | [ W. Xu, L. Chen and S. Chen, etc, An impulsive state feedback control model for releasing white-headed langurs in captive to the wild, Commun. Nonlinear Sci., 34 (2016), 199-209. |
[24] | [ Y. Ye, Limit Cycle Theory, Shanghai Science and Technology Press, Shanghai, 1984. (in Chinese) |
[25] | [ S. Yuan, X. Ji and H. Zhu, Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations, Mathematical Biosciences and Engineering, 14 (2017), 1477-1498. |
[26] | [ Y. Zhang, Y. Li, Q. Zhang and A. Li, Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules, Physica A, 501 (2018), 178-187. |
[27] | [ M. Zhang, G. Song and L. Chen, A state feedback impulse model for computer worm control, Nonlinear Dynam., 85 (2016), 1561-1569. |
[28] | [ Y. Zhang, Y. Zheng, F. Zhao and X. Liu, Dynamical analysis in a stochastic bioeconomic model with stage-structuring, Nonlinear Dynamics, 84 (2016), 1113-1121. |
[29] | [ M. Zhu, X. Guo and Z. Lin, The risk index for an SIR epidemic model and spatial spreading of the infectious disease, Mathematical Biosciences and Engineering, 14 (2017), 1565-1583. |
[30] | [ C. C. Zou, D. Towsley and W. Gong, On the performance of Internet worm scanning strategies, Performance Evaluation, 63 (2006), 700-723. |
[31] | [ C. C. Zou, D. Towsley and W. Gong, On the performance of Internet worm scanning strategies, Performance Evaluation, 63 (2006), 700-723. |