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Keywords:
macro traffic flow; curves; ramps; bifurcation analysis
Summary:
A macroscopic traffic flow model considering the effects of curves, ramps, and adverse weather is proposed, and nonlinear bifurcation theory is used to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. Firstly, the stability conditions of the model shock wave were investigated using the linear stability analysis method. Then, the long-wave mode at the coarse-grained scale is considered, and the model is analyzed using the reduced perturbation method to obtain the Korteweg-de Vries (KdV) equation of the model in the sub-stable region. In addition, the type of equilibrium points and their stability are discussed by using bifurcation analysis, and a theoretical derivation proves the existence of Hopf bifurcation and saddle-knot bifurcation in the model. Finally, the simulation density spatio-temporal and phase plane diagrams verify that the model can describe traffic phenomena such as traffic congestion and stop-and-go traffic in real traffic, providing a theoretical basis for the prevention of traffic congestion.
References:
[1] Ai, W.-H., Shi, Z.-K., Liu, D.-W.: Bifurcation analysis of a speed gradient continuum traffic flow model. Physica A 437 (2015), 418-429. DOI 10.1016/j.physa.2015.06.004 | MR 3371710 | Zbl 1400.90088
[2] Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E (3) 51 (1995), 1035-1042. DOI 10.1103/PhysRevE.51.1035
[3] Cao, J. F., Han, C. Z., Fang, Y. W.: Nonlinear Systems Theory and Application. Xi'an Jiao Tong University Press, Xi'an (2006), ISBN 7-5605-2140-1\nopunct Chinese.
[4] Carrillo, F. A., Delgado, J., Saavedra, P., Velasco, R. M., Verduzco, F.: Traveling waves, catastrophes and bifurcations in a generic second order traffic flow model. Int. J. Bifurcation Chaos Appl. Sci. Eng. 23 (2013), Article ID 1350191, 15 pages. DOI 10.1142/S0218127413501915 | MR 3158306 | Zbl 1284.90012
[5] Chen, B., Sun, D., Zhou, J., Wong, W., Ding, Z.: A future intelligent traffic system with mixed autonomous vehicles and human-driven vehicles. Inform. Sci. 529 (2020), 59-72. DOI 10.1016/j.ins.2020.02.009 | MR 4093031
[6] Cui, N., Chen, B., Zhang, K., Zhang, Y., Liu, X., Zhou, J.: Effects of route guidance strategies on traffic emissions in intelligent transportation systems. Physica A 513 (2019), 32-44. DOI 10.1016/j.physa.2018.08.009
[7] Daganzo, C. F., Laval, J. A.: Moving bottlenecks: A numerical method that converges in flows. Transp. Res., Part B 39 (2005), 855-863. DOI 10.1016/j.trb.2004.10.004
[8] Delgado, J., Saavedra, P.: Global bifurcation diagram for the Kerner-Konhäuser traffic flow model. Int. J. Bifurcation Chaos Appl. Sci. Eng. 25 (2015), Article ID 1550064, 18 pages. DOI 10.1142/S0218127415500649 | MR 3349898 | Zbl 1317.34074
[9] Gupta, A. K., Dhiman, I.: Phase diagram of a continuum traffic flow model with a static bottleneck. Nonlinear Dyn. 79 (2015), 663-671. DOI 10.1007/s11071-014-1693-6 | MR 3302725
[10] Gupta, A. K., Katiyar, V. K.: Analyses of shock waves and jams in traffic flow. J. Phys. A, Math. Gen. 38 (2005), 4069-4083. DOI 10.1088/0305-4470/38/19/002 | MR 2145802 | Zbl 1086.90013
[11] Gupta, A. K., Katiyar, V. K.: A new anisotropic continuum model for traffic flow. Physica A 368 (2006), 551-559. DOI 10.1016/j.physa.2005.12.036
[12] Gupta, A. K., Katiyar, V. K.: Phase transition of traffic states with on-ramp. Physica A 371 (2006), 674-682. DOI 10.1016/j.physa.2006.03.061
[13] Gupta, A. K., Redhu, P.: Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference. Phys. Lett., A 377 (2013), 2027-2033. DOI 10.1016/j.physleta.2013.06.009 | MR 3083138 | Zbl 1297.90017
[14] Gupta, A. K., Sharma, S.: Nonlinear analysis of traffic jams in an anisotropic continuum model. Chin. Phys. B 19 (2010), Article ID 110503, 9 pages. DOI 10.1088/1674-1056/19/11/110503
[15] Gupta, A. K., Sharma, S.: Analysis of the wave properties of a new two-lane continuum model with the coupling effect. Chin. Phys. B 21 (2012), Article ID 015201, 15 pages. DOI 10.1088/1674-1056/21/1/015201
[16] Igarashi, Y., Itoh, K., Nakanishi, K., Ogura, K., Yokokawa, K.: Quasi-solitons in dissipative systems and exactly solvable lattice models. Phys. Rev. Lett. 83 (1999), 718-721. DOI 10.1103/PhysRevLett.83.718
[17] Igarashi, Y., Itoh, K., Nakanishi, K., Ogura, K., Yokokawa, K.: Bifurcation phenomena in the optimal velocity model for traffic flow. Phys. Rev. E (3) 64 (2001), Article ID 047102. DOI 10.1103/PhysRevE.64.047102
[18] Jiang, R., Wu, Q., Zhu, Z.: Full velocity difference model for a car-following theory. Phys. Rev. E (3) 64 (2001), Article ID 017101. DOI 10.1103/PhysRevE.64.017101 | MR 2998582
[19] Jiang, R., Wu, Q.-S., Zhu, Z.-J.: A new continuum model for traffic flow and numerical tests. Transp. Res., Part B 36 (2002), 405-419. DOI 10.1016/S0191-2615(01)00010-8
[20] Kerner, B. S., Konhäuser, P.: Cluster effect in initially homogeneous traffic flow. Phys. Rev. E (3) 48 (1993), 2335-2338. DOI 10.1103/PhysRevE.48.R2335
[21] Kuznetsov, Y. A.: Bifurcations of equilibria and periodic orbits in $n$-dimensional dynamical systems. Elements of Applied Bifurcation Theory Applied Mathematical Sciences 112. Springer, New York (1998), 151-194. DOI 10.1007/978-0-387-22710-8_5 | MR 1711790 | Zbl 0914.58025
[22] Lei, L., Wang, Z., Wu, Y.: Modeling and analyzing for a novel continuum model considering self-stabilizing control on curved road with slope. CMES, Comput. Model. Eng. Sci. 131 (2022), 1815-1830. DOI 10.32604/cmes.2022.019855
[23] Ling, D., Jian, X. P.: Stability and bifurcation characteristics of a class of nonlinear vehicle following model. J. Traffic and Transportation Engineering and Information 7 (2009), 6-11.
[24] Ma, G., Ma, M., Liang, S., Wang, Y., Guo, H.: Nonlinear analysis of the car-following model considering headway changes with memory and backward looking effect. Physica A 562 (2021), Article ID 125303, 12 pages. DOI 10.1016/j.physa.2020.125303 | MR 4157710 | Zbl 07542618
[25] Ma, G., Ma, M., Liang, S., Wang, Y., Zhang, Y.: An improved car-following model accounting for the time-delayed velocity difference and backward looking effect. Commun. Nonlinear Sci. Numer. Simul. 85 (2020), Article ID 105221, 10 pages. DOI 10.1016/j.cnsns.2020.105221 | MR 4065383 | Zbl 1452.65169
[26] Meng, X. P., Yan, L. Y.: Stability analysis in a curved road traffic flow model based on control theory. Asian J. Control 19 (2017), 1844-1853. DOI 10.1002/asjc.1505 | MR 3704494 | Zbl 1386.93217
[27] Orosz, G., Wilson, R. E., Krauskopf, B.: Global bifurcation investigation of an optimal velocity traffic model with driver reaction time. Phys. Rev. E (3) 70 (2004), Article ID 026207, 10 pages. DOI 10.1103/PhysRevE.70.026207 | MR 2129214
[28] Redhu, P., Gupta, A. K.: Delayed-feedback control in a Lattice hydrodynamic model. Commun. Nonlinear Sci. Numer. Simul. 27 (2015), 263-270. DOI 10.1016/j.cnsns.2015.03.015 | MR 3341560 | Zbl 1457.93068
[29] Zeng, J., Qian, Y., Xu, D., Jia, Z., Huang, Z.: Impact of road bends on traffic flow in a single-lane traffic system. Math. Probl. Eng. 2014 (2014), Article ID 218465, 6 pages. DOI 10.1155/2014/218465 | MR 3166824 | Zbl 1407.90103
[30] Zhai, C., Wu, W.: A new car-following model considering driver's characteristics and traffic jerk. Nonlinear Dyn. 93 (2018), 2185-2199. DOI 10.1007/s11071-018-4318-7
[31] Zhai, C., Wu, W.: Car-following model based delay feedback control method with the gyroidal road. Int. J. Mod. Phys. C 30 (2019), Article ID 1950073, 14 pages. DOI 10.1142/S0129183119500736 | MR 4015821
[32] Zhai, C., Wu, W.: Lattice hydrodynamic model-based feedback control method with traffic interruption probability. Mod. Phys. Lett. B 33 (2019), Article ID 1950273, 16 pages. DOI 10.1142/S0217984919502737 | MR 3993691
[33] Zhai, C., Wu, W.: A modified two-dimensional triangular lattice model under honk environment. Int. J. Mod. Phys. C 31 (2020), Article ID 2050089, 16 pages. DOI 10.1142/S0129183120500898 | MR 4119105
[34] Zhai, C., Wu, W.: Lattice hydrodynamic modeling with continuous self-delayed traffic flux integral and vehicle overtaking effect. Mod. Phys. Lett. B 34 (2020), Article ID 2050071, 15 pages. DOI 10.1142/S0217984920500712 | MR 4068029
[35] Zhai, C., Wu, W.: A macro traffic flow model with headway variation tendency and bounded rationality. Mod. Phys. Lett. B 35 (2021), Article ID 2150054, 15 pages. DOI 10.1142/S0217984921500548 | MR 4202802
[36] Zhai, C., Wu, W.: Designing continuous delay feedback control for lattice hydrodynamic model under cyber-attacks and connected vehicle environment. Commun. Nonlinear Sci. Numer. Simul. 95 (2021), Article ID 105667, 18 pages. DOI 10.1016/j.cnsns.2020.105667 | MR 4192012 | Zbl 1456.82635
[37] Zhang, P., Xue, Y., Zhang, Y.-C., Wang, X., Cen, B.-L.: A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes. Mod. Phys. Lett. B 34 (2020), Article ID 2050217, 18 pages. DOI 10.1142/S0217984920502176 | MR 4128734
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