Bifurcation analysis of a speed gradient continuum traffic flow model

Ai, Wenhuan; Shi, Zhongke; Liu, Dawei

doi:10.1016/j.physa.2015.06.004

Cited by 30 publications

(6 citation statements)

References 21 publications

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“…Table 1. Types of equilibrium points for linear dynamical systems (11). The linear system( 11) is unstable at the saddle point when   z…”

Section: Model and It's Derivationmentioning

confidence: 99%

“…). According to the Hartman-Gorban linearization theorem [11] , when the eigenvalues of nonlinear system have non-zero real parts, that is, the equilibrium point is a non central point, the stability of nonlinear system and linear system at equilibrium point is consistent. It is difficult to appear a central point in the traffic flow model, so we discussed it here.…”

Section: Model and It's Derivationmentioning

confidence: 99%

“…Types and stabilities of some equilibrium points of linear system (11) with the given model parameters, where Using the two sets of parameters in table 2 to simulate the system (10) respectively. We can obtain the phase plane diagrams near the equilibrium point as shown in figure 1.…”

Section: Numerical Simulationmentioning

confidence: 99%

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Stability analysis of a viscous continuous traffic flow model

Tian

2022

ITM Web Conf.

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This paper studies the stability of a speed gradient continuous traffic flow model, which is proposed by Ge et al and based on TVDM. The nonlinear and linear systems of traveling wave solutions of the model equation are derived by traveling wave substitution. And the types of equilibrium points and it’s stability are analyzed theoretically. Finally, the phase plane diagram is obtained through simulation, and the global distribution structure of the trajectories is analyzed. The results show that the numerical results are consistent with the theoretical analysis, so some nonlinear traffic phenomena can be analyzed and predicted from the perspective of global stability.

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“…Table 1. Types of equilibrium points for linear dynamical systems (11). The linear system( 11) is unstable at the saddle point when   z…”

Section: Model and It's Derivationmentioning

confidence: 99%

Section: Model and It's Derivationmentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis of a viscous continuous traffic flow model

Tian

2022

ITM Web Conf.

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“…As described in this section, a numerical simulation is performed to study the bifurcation characteristics of uphill and downhill traffic flows. The parameters * ( , ) ( 1.371,0.2) cq  [45] selected to derive the equilibrium point specified in Section 5 are summarized in Table 2. According to the nonlinear stability theory, the stability of the equilibrium point is confirmed.…”

Section: Hopf Bifurcation Of the Traffic Systemmentioning

confidence: 99%

“…The impact of multiple time delays and other model parameters on the Hopf bifurcation in various existing car-following models with delays was discussed. In 2015, Ai et al [45] considered that bifurcation corresponds to traffic jams by the bifurcation analysis for a speed gradient macro continuum traffic flow model. More recently, Miura et al [46] observed macroscopic collective phenomenon that occur only in multi-body systems while studying bifurcations in optimal velocity models.…”

Section: Introductionmentioning

confidence: 99%

Global stability and bifurcation of macroscopic traffic flow models for upslope and downslope

et al. 2022

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A macro continuum model of the traffic flow is derived from a micro car-following model that considers both the upslope and downslope by using the transformation relationship between macro-and micro variables. The perturbation propagation characteristics and stability conditions of the macroscopic continuum equation are discussed. For uniform flow in the initial equilibrium state, the stability conditions reveal that as the slope angle increased under the action of a small disturbance, the upslope stability increases and downslope stability decreases. Moreover, under a large disturbance, the global stability analysis is carried out by using the wavefront expansion technique for uniform flow in the initial equilibrium state. For the initial nonuniform flow, nonlinear bifurcation analysis is conducted at the equilibrium point. Subcritical Hopf bifurcation exists when the traffic flow state changes，thus the limit cycle formed by the Hopf bifurcation is unstable. Simulation results verify the stability conditions of the model and determine the critical density range. The numerical simulation results show the existence of critical Hopf bifurcation in phase space, and the spiral saddle point varies with the slope angle. Furthermore, the impact of the angle of both the upslope and downslope on the evolution of density waves is investigated.

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Phase Plane Analysis of Traffic Flow Evolution Based on a Macroscopic Traffic Flow Model

Xing

et al. 2020

IFIP Advances in Information and Communication Technology

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In this paper, a new phase plane analysis method is proposed to study the nonlinear phenomena of traffic flow. Most of the papers describe only one or several traffic phenomena and do not analyze all of them from the perspective of system stability. Therefore, this paper studies the phase plane analysis of traffic flow phenomenon from the perspective of traffic system stability, and describes various complicated nonlinear traffic phenomena through phase plane analysis.

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Bifurcation analysis of a speed gradient continuum traffic flow model

Cited by 30 publications

References 21 publications

Stability analysis of a viscous continuous traffic flow model

Stability analysis of a viscous continuous traffic flow model

Global stability and bifurcation of macroscopic traffic flow models for upslope and downslope

Phase Plane Analysis of Traffic Flow Evolution Based on a Macroscopic Traffic Flow Model

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