[1]

Huang L, Zhai C, Wang H, Zhang R, Qiu Z, et al. 2020. Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city. Journal of Environmental Management 256:109975

doi: 10.1016/j.jenvman.2019.109975
[2]

Zhai C, Wu W. 2021. Self-delayed feedback car-following control with the velocity uncertainty of preceding vehicles on gradient roads. Nonlinear Dynamics 106:3379−400

doi: 10.1007/s11071-021-06970-7
[3]

Zhai C, Wu W. 2018. A new car-following model considering driver’s characteristics and traffic jerk. Nonlinear Dynamics 93:2185−99

doi: 10.1007/s11071-018-4318-7
[4]

Ma M, Ma G, Liang S. 2021. Density waves in car-following model for autonomous vehicles with backward looking effect. Applied Mathematical Modelling 94:1−12

doi: 10.1016/j.apm.2021.01.002
[5]

Ma G, Ma M, Liang S, Wang Y, Guo H. 2021. Nonlinear analysis of the car-following model considering headway changes with memory and backward looking effect. Physica A: Statistical Mechanics and Its Applications 562:125303

doi: 10.1016/j.physa.2020.125303
[6]

Ma G, Ma M, Liang S, Wang Y, Zhang Y. 2020. An improved car-following model accounting for the time-delayed velocity difference and backward looking effect. Communications in Nonlinear Science and Numerical Simulation 85:105221

doi: 10.1016/j.cnsns.2020.105221
[7]

Jiang Y, Wang S, Yao Z, Zhao B, Wang Y. 2021. A cellular automata model for mixed traffic flow considering the driving behavior of connected automated vehicle platoons. Physica A:Statistical Mechanics and Its Applications 582:126262

doi: 10.1016/j.physa.2021.126262
[8]

Chen B, Sun D, Zhou J, Wong W, Ding Z. 2020. A future intelligent traffic system with mixed autonomous vehicles and human-driven vehicles. Information Sciences 529:59−72

doi: 10.1016/j.ins.2020.02.009
[9]

Zhai C, Wu W. 2021. Designing continuous delay feedback control for lattice hydrodynamic model under cyber-attacks and connected vehicle environment. Communications in Nonlinear Science and Numerical Simulation 95:105667

doi: 10.1016/j.cnsns.2020.105667
[10]

Redhu P, Gupta AK. 2015. Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing. Physica A: Statistical Mechanics and Its Applications 421:249−60

doi: 10.1016/j.physa.2014.11.037
[11]

Kaur D, Sharma S. 2020. A new two-lane lattice model by considering predictive effect in traffic flow. Physica A: Statistical Mechanics and Its Applications 539:122913

doi: 10.1016/j.physa.2019.122913
[12]

Sharma S. 2015. Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior. Physica A: Statistical Mechanics and Its Applications 421:401−11

doi: 10.1016/j.physa.2014.11.003
[13]

Kaur R, Sharma S. 2017. Analysis of driver's characteristics on a curved road in a lattice model. Physica A: Statistical Mechanics and Its Applications 471:59−67

doi: 10.1016/j.physa.2016.11.116
[14]

Redhu P, Gupta AK. 2015. Delayed-feedback control in a Lattice hydrodynamic model. Communications in Nonlinear Science and Numerical Simulation 27:263−70

doi: 10.1016/j.cnsns.2015.03.015
[15]

Kaur R, Sharma S. 2018. Analyses of lattice hydrodynamic model using delayed feedback control with passing. Physica A:Statistical Mechanics and Its Applications 510:446−55

doi: 10.1016/j.physa.2018.06.118
[16]

Kaur R, Sharma S. 2018. Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles. Physics Letters A 382:1449−55

doi: 10.1016/j.physleta.2018.03.045
[17]

Helbing D. 1995. Improved fluid-dynamic model for vehicular traffic. Physical Review E 51:3164−69

doi: 10.1103/physreve.51.3164
[18]

Lighthill M, Whitham G. 1955. On kinematic waves I. Flood movement in long rivers. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 229:281−316

doi: 10.1098/rspa.1955.0088
[19]

Lighthill MJ, Whitham GB. 1955. On kinematic waves II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 229:317−45

doi: 10.1098/rspa.1955.0089
[20]

Richards PI. 1956. Shock waves on the highway. Operations Research 4:42−51

doi: 10.1287/opre.4.1.42
[21]

Payne H. 1971. Models of freeway traffic and control: mathematical models of public systems. Simulation Council Proceeding Series 1(1):51−61

[22]

Daganzo CF. 1995. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B: Methodological 29:277−86

doi: 10.1016/0191-2615(95)00007-z
[23]

Zhang HM. 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B:Methodological 36:275−90

doi: 10.1016/s0191-2615(00)00050-3
[24]

Jiang R, Wu Q, Zhu Z. 2002. A new continuum model for traffic flow and numerical tests. Transportation Research Part B:Methodological 36:405−19

doi: 10.1016/s0191-2615(01)00010-8
[25]

Wang Z, Zhu W. 2023. Effects of electronic throttle dynamics in non-equilibrium heterogeneous traffic flow without lane discipline. Applied Mathematical Modelling 116:673−94

doi: 10.1016/j.apm.2022.12.005
[26]

Ren W, Cheng R, Ge H. 2021. Bifurcation analysis of a heterogeneous continuum traffic flow model. Applied Mathematical Modelling 94:369−87

doi: 10.1016/j.apm.2021.01.025
[27]

Ren W, Cheng R, Ge H. 2021. Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory. Applied Mathematics and Computation 401:126079

doi: 10.1016/j.amc.2021.126079
[28]

Sun L, Jafaripournimchahi A, Hu W. 2020. A forward-looking anticipative viscous high-order continuum model considering two leading vehicles for traffic flow through wireless V2X communication in autonomous and connected vehicle environment. Physica A: Statistical Mechanics and Its Applications 556:124589

doi: 10.1016/j.physa.2020.124589
[29]

Sun L, Jafaripournimchahi A, Kornhauser A, Hu W. 2020. A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles. Physica A: Statistical Mechanics and Its Applications 547:123829

doi: 10.1016/j.physa.2019.123829
[30]

Liu H, Cheng R, Zhu K, Ge H. 2016. The study for continuum model considering traffic jerk effect. Nonlinear Dynamics 83:57−64

doi: 10.1007/s11071-015-2307-7
[31]

Cheng R, Ge H, Wang J. 2018. The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect. Applied Mathematics and Computation 332:493−505

doi: 10.1016/j.amc.2018.03.077
[32]

Lyu H, Cheng R, Ge H. 2022. Bifurcation analysis of an extended macro model considering time delay and anticipation effect. Physica A: Statistical Mechanics and Its Applications 585:126434

doi: 10.1016/j.physa.2021.126434
[33]

Jafaripournimchahi A, Cai Y, Wang H, Sun L, Yang B. 2022. Stability analysis of delayed-feedback control effect in the continuum traffic flow of autonomous vehicles without V2I communication. Physica A: Statistical Mechanics and Its Applications 605:127975

doi: 10.1016/j.physa.2022.127975
[34]

Liu Z, Cheng R, Ge H. 2019. Research on preceding vehicle's taillight effect and energy consumption in an extended macro traffic model. Physica A: Statistical Mechanics and Its Applications 525:304−14

doi: 10.1016/j.physa.2019.03.051
[35]

Zhai C, Wu W. 2021. A continuous traffic flow model considering predictive headway variation and preceding vehicle's taillight effect. Physica A: Statistical Mechanics and Its Applications 584:126364

doi: 10.1016/j.physa.2021.126364
[36]

Jiao Y, Ge H, Cheng R. 2019. Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect. Physica A: Statistical Mechanics and Its Applications 535:122362

doi: 10.1016/j.physa.2019.122362
[37]

Wang Z, Ge H, Cheng R. 2018. Nonlinear analysis for a modified continuum model considering driver's memory and backward looking effect. Physica A: Statistical Mechanics and Its Applications 508:18−27

doi: 10.1016/j.physa.2018.05.072
[38]

Cheng R, Ge H, Wang J. 2017. An improved continuum model for traffic flow considering driver's memory during a period of time and numerical tests. Physics Letters A 381:2792−800

doi: 10.1016/j.physleta.2017.06.047
[39]

Zhai Q, Ge H, Cheng R. 2018. An extended continuum model considering optimal velocity change with memory and numerical tests. Physica A: Statistical Mechanics and Its Applications 490:774−85

doi: 10.1016/j.physa.2017.08.152
[40]

Cheng R, Ge H, Sun F, Wang J. 2018. An extended macro model accounting for acceleration changes with memory and numerical tests. Physica A: Statistical Mechanics and Its Applications 506:270−83

doi: 10.1016/j.physa.2018.04.060
[41]

Zhai C, Wu W. 2018. Analysis of drivers' characteristics on continuum model with traffic jerk effect. Physics Letters A 382:3381−92

doi: 10.1016/j.physleta.2018.09.029
[42]

Cheng R, Ge H, Wang J. 2017. An extended continuum model accounting for the driver's timid and aggressive attributions. Physics Letters A 381:1302−12

doi: 10.1016/j.physleta.2017.02.018
[43]

Zhai C, Wu W. 2022. A continuum model considering the uncertain velocity of preceding vehicles on gradient highways. Physica A: Statistical Mechanics and Its Applications 588:126561

doi: 10.1016/j.physa.2021.126561
[44]

Chen J, Shi Z, Hu Y, Yu L, Fang Y. 2013. An extended macroscopic model for traffic flow on a highway with slopes. International Journal of Modern Physics C 24:1350061

doi: 10.1142/s0129183113500617
[45]

Liu Z, Ge H, Cheng R. 2018. KdV–Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road. Physica A: Statistical Mechanics and Its Applications 503:1218−27

doi: 10.1016/j.physa.2018.08.106
[46]

Xue Y, Zhang Y, Fan D, Zhang P, He H. 2019. An extended macroscopic model for traffic flow on curved road and its numerical simulation. Nonlinear Dynamics 95:3295−307

doi: 10.1007/s11071-018-04756-y
[47]

Guan X, Cheng R, Ge H. 2021. Bifurcation control of optimal velocity model through anticipated effect and response time-delay feedback methods. Physica A: Statistical Mechanics and Its Applications 574:125972

doi: 10.1016/j.physa.2021.125972
[48]

Cheng R, Ge H, Wang J. 2017. KdV–Burgers equation in a new continuum model based on full velocity difference model considering anticipation effect. Physica A: Statistical Mechanics and Its Applications 481:52−9

doi: 10.1016/j.physa.2017.04.004
[49]

Ngoduy D. 2021. Noise-induced instability of a class of stochastic higher order continuum traffic models. Transportation Research Part B: Methodological 150:260−78

doi: 10.1016/j.trb.2021.06.013
[50]

Bouadi M, Jia B, Jiang R, Li X, Gao Z. 2022. Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations. Transportation Research Part B: Methodological 164:193−209

doi: 10.1016/j.trb.2022.09.001
[51]

Wang Z, Ge H, Cheng R. 2020. An extended macro model accounting for the driver’s timid and aggressive attributions and bounded rationality. Physica A: Statistical Mechanics and Its Applications 540:122988

doi: 10.1016/j.physa.2019.122988
[52]

Tang T, Huang H, Shang H. 2017. An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests. Physica A: Statistical Mechanics and Its Applications 468:322−33

doi: 10.1016/j.physa.2016.10.092
[53]

Zhu W, Yu R. 2014. A new car-following model considering the related factors of a gyroidal road. Physica A: Statistical Mechanics and Its Applications 393:101−11

doi: 10.1016/j.physa.2013.09.049
[54]

Zhai C, Wu W. 2019. Car-following model based delay feedback control method with the gyroidal road. International Journal of Modern Physics C 30:1950073

doi: 10.1142/s0129183119500736
[55]

Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y. 1995. Dynamical model of traffic congestion and numerical simulation. Physical Review E 51:1035−42

doi: 10.1103/physreve.51.1035
[56]

Helbing D, Tilch B. 1998. Generalized force model of traffic dynamics. Physical Review E 58:133−38

doi: 10.1103/physreve.58.133
[57]

Jiang R, Wu Q, Zhu Z. 2001. Full velocity difference model for a car-following theory. Physical Review E 64:017101

doi: 10.1103/PhysRevE.64.017101
[58]

Sun D, Kang Y, Yang S. 2015. A novel car following model considering average speed of preceding vehicles group. Physica A: Statistical Mechanics and Its Applications 436:103−9

doi: 10.1016/j.physa.2015.04.028
[59]

Kuang H, Yang F, Wang M, Peng G, Li X. 2021. Multi-anticipative average flux effect in the lattice hydrodynamic model. IEEE Access 9:35279−86

doi: 10.1109/access.2021.3060080
[60]

Berg P, Mason A, Woods A. 2000. Continuum approach to car-following models. Physical Review E 61:1056−66

doi: 10.1103/physreve.61.1056
[61]

Fan E. 2000. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A 277:212−18

doi: 10.1016/s0375-9601(00)00725-8
[62]

Elwakil SA, El-Labany SK, Zahran MA, Sabry R. 2005. Modified extended tanh-function method and its applications to nonlinear equations. Applied Mathematics and Computation 161:403−12

doi: 10.1016/j.amc.2003.12.035
[63]

Jiang R, Wu Q, Zhu Z. 2001. A new dynamics model for traffic flow. Chinese Science Bulletin 46:345−48

doi: 10.1007/BF03187201
[64]

Castillo JMD, Benítez FG. 1995. On the functional form of the speed-density relationship—I: general theory. Transportation Research Part B: Methodological 29:373−89

doi: 10.1016/0191-2615(95)00008-2
[65]

Herrmann M, Kerner BS. 1998. Local cluster effect in different traffic flow models. Physica A: Statistical Mechanics and Its Applications 255:163−88

doi: 10.1016/s0378-4371(98)00102-2
[66]

Kerner BS, Konhäuser P. 1993. Cluster effect in initially homogeneous traffic flow. Physical Review E 48:R2335−R2338

doi: 10.1103/physreve.48.r2335