BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS*

doi:10.1007/s10473-023-0621-6

Abstract

Abstract: A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper, and a novel strategy to control the bifurcation of this model is proposed. First, Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller. Then, a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller. Finally, in order to verify the theoretical results, some numerical simulations are given.

Key words: rumor spreading, fractional-order, time delay, bifurcation control

CLC Number:

34A08

Maolin YE, Haijun JIANG. BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS^*[J].Acta mathematica scientia,Series B, 2023, 43(6): 2662-2682.

Trendmd

References

[1] DiFonzo N. Rumour research can douse digital wildfires. Nature, 2013, 493(7431): 135
[2] Malamut S, Dawes M, Xie H. Characteristics of rumors and rumor victims in early adolescence: Rumor content and social impact. Review of Social Development, 2018, 27(3): 601-618
[3] Sääksjärvi M, Gill T, Hultink E. How rumors and preannouncements foster curiosity toward products. Eur J Innov Manag, 2017, 20(3): 350-371
[4] Daley D, Kendall D. Epidemics and rumours. Nature, 1964, 204: 1118
[5] Daley D, Kendall D. Stochastic rumours. IMA J Appl Math, 1965, 1(1): 42-55
[6] Maki D, Thomson M.Mathematical Models and Applications. Englewood Cliffs: Prentice-Hall, 1973
[7] Wang H, Deng L, Xie F, Xu H, Han J.A new rumor propagation model on SNS structure. IEEE International Conference, 2012: 499-503
[8] Zhao L, Cui H, Qiu X, Wang X, Wang J. SIR rumor spreading model in the new media age. Phys A, 2013, 392(4): 995-1003
[9] Zhu L, Zhou X, Li Y. Global dynamics analysis and control of a rumor spreading model in online social networks. Phys A, 2019, 526: 120903
[10] Chen G. ILSCR rumor spreading model to discuss the control of rumor spreading in emergency. Phys A, 2019, 522: 88-97
[11] Wang J, Jiang H, Ma T, Hu C. Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism. Chaos, Soliton Fract, 2019, 126: 148-157
[12] Li J, Jiang H, Mei X, Hu C, Zhang G. Dynamical analysis of rumor spreading model in multi-lingual environment and heterogeneous complex networks. Inform Sciences, 2020, 536: 391-408
[13] Afassinou K. Analysis of the impact of education rate on the rumor spreading mechanism. Phys A, 2014, 414: 43-52
[14] Zhu L, Zhou X, Li Y. Global dynamics analysis and control of a rumor spreading model in online social networks. Phys A, 2019, 526: 120903
[15] Zhu L, Liu W, Zhang Z. Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function. Appl Math Comput, 2020, 370: 124925
[16] Yu S, Yu Z, Jiang H, Yang S. The dynamics and control of 2I2SR rumor spreading models in multilingual online social networks. Inform Sciences, 2020, 581(1): 18-41
[17] Zhu L, Guan G. Dynamical analysis of a rumor spreading model with self-discrimination and time delay in complex networks. Phys A, 2019, 533: 121953
[18] Ankur J, Joydip D, Vijay G. Rumor model on homogeneous social network incorporating delay in expert intervention and government action. Commun Nonlinear Sci, 2020, 84: 105189
[19] Wang J, Jiang H, Hu C, Yu Z, Li J. Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism. Chaos Soliton Fract, 2021, 153: 111464
[20] Tao B, Xiao M, Jiang G, Cao J. Stability, bifurcation prediction and optimal control of a delayed integer-order small-world network based on the fractional-order PD control policy of variable order. J Franklin I, 2020, 357: 10288-10311
[21] Xiao M, Zheng W, Cao J. Bifurcation control of a congestion control model via state feedback. Int J Bifurcat Chaos, 2013, 23(6): 1330018
[22] Cheng Z, Cao J. Hybrid control of Hopf bifurcation in complex networks with delays. Neurocomputing, 2014, 131: 164-170
[23] Zhou Z, Wang F, Zheng X. Analysis and discretization for an optimal control problem of a variable-coefficient Riesz-fractional diffusion equation with pointwise control constraints. Acta Mathematica Scientia, 2023, 43B(2): 640-654
[24] Telke C, Beitelschmidt M. Edge detection based on fractional order differentiation and its application to railway track images. Proceedings in Applied Mathematics and Mechanics, 2015, 15(1): 671-672
[25] Jspa E, Atmb J. Fractional order dynamics in a GA planner. Signal Process, 2003, 83(11): 2377-2386
[26] Zeng Z, Chen Y. A local discontinuous Galerkin method for time-fractional diffusion equations. Acta Mathematica Scientia, 2023, 43B(2): 839-854
[27] Wang X, Wang Z, Huang X, Li Y. Dynamic analysis of a delayed fractional-order SIR model with saturated incidence and treatment functions. Int J Bifurcat Chaos, 2018, 28(14): 1850180
[28] Wang X, Wang Z, Xia J. Stability and bifurcation control of a delayed fractional-order eco-epidemiological model with incommensurate orders. J Franklin I, 2019, 356(15): 8278-8295
[29] Xiao M, Zheng W, Lin J, Jiang G, Zhao L, Cao J. Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks. J Franklin I, 2017, 354(17): 7643-7667
[30] Shu P.Effects of memory on information spreading in complex networks. IEEE International Conference, 2014, 554-556
[31] Liu F, Meerschaert M, Momani S, et al.Fractional Differential Equations. San Diego: Academic Press, 1999
[32] Deng W, Li C, Lü J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynam, 2006, 48(4): 409-416
[33] Li C, Zhao Z. Asymptotical stability analysis of linear fractional differential systems. Journal of Shanghai University, 2009, 13(3): 197-206
[34] Huang C, Li H, Cao J. A novel strategy of bifurcation control for a delayed fractional predator-prey model. Appl Math Comput, 2019, 347: 808-838
[35] Naik P, Jian Z, Owolabi K. Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control. Chaos Soliton Fract, 2020, 137: 1-30
[36] Javidi M, Heris M, Ahmad B. A predictor-corrector scheme for solving nonlinear fractional differential equations with uniform and nonuniform meshes. Int J Model Simul Sc, 2019, 10(5): 1950033
[37] Zhang Y, Xu J. A rumor spreading model considering the cumulative effects of memory. Discrete Dyn Nat Soc, 2015, 2015: 1-11
[38] Singh J. A new analysis for fractional rumor spreading dynamical model in a social network with Mittag-Leffler law. Chaos, 2019, 29(1): 013137
[39] Ren G, Yu Y, Lu Z, Chen W.A fractional order model for rumor spreading in mobile social networks from a stochastic process. 9th International Conference on Systems and Control, IEEE, 2021: 312-318
[40] Huang C, Li H, Cao J. A novel strategy of bifurcation control for a delayed fractional predator-prey model. Appl Math Comput, 2019, 347: 808-838
[41] Zhu L, Zhao H, Wang X. Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control. Commun Nonlinear Sci, 2015, 22(1-3): 747-768

BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS^*

Abstract

Cite this article

share this article

References

Related Articles 7

Metrics

Comments

Recommended 10

[1]	Ruihong LI, Huaiqin WU, Jinde CAO. IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS [J]. Acta mathematica scientia,Series B, 2022, 42(2): 737-754.
[2]	Wenjun LIU, Dongqin CHEN, Zhijing CHEN. LONG-TIME BEHAVIOR FOR A THERMOELASTIC MICROBEAM PROBLEM WITH TIME DELAY AND THE COLEMAN-GURTIN THERMAL LAW [J]. Acta mathematica scientia,Series B, 2021, 41(2): 609-632.
[3]	Suiming SHANG, Yu TIAN, Yajing ZHANG. FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY [J]. Acta mathematica scientia,Series B, 2017, 37(6): 1705-1726.
[4]	GUO Wan-Li, XIAO Hai-Jun, CHEN Shi-Hua. CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY [J]. Acta mathematica scientia,Series B, 2014, 34(2): 453-465.
[5]	QIAO Mei-Hong, QI Huan, CHEN Ying-Chun. QUALITATIVE ANALYSIS OF HEPATITIS B VIRUS INFECTION MODEL WITH IMPULSIVE VACCINATION AND TIME DELAY [J]. Acta mathematica scientia,Series B, 2011, 31(3): 1020-1034.
[6]	Zhen Jin; Ma Zhien; Han Maoan. GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS [J]. Acta mathematica scientia,Series B, 2006, 26(2): 291-306.
[7]	XU Rui, CHEN Lan-Sun. PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS [J]. Acta mathematica scientia,Series B, 2002, 22(4): 533-541.