Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

The time-dependent Ginzburg-Landau equation for the two-velocity difference model

A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow.Based on the two-velocity difference model,the time-dependent Ginzburg-Landau (TDGL) equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method.The corresponding two solutions,the uniform and the kink solutions,are given.The coexisting curve,spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential.The modified Korteweg de Vries (mKdV) equation around the critical point is derived by using the reductive perturbation method and its kink-antikink solution is also obtained.The relation between the TDGL equation and the mKdV equation is shown.The simulation result is consistent with the nonlinear analytical result.     

一类相对转动非线性动力学模型的近似解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词： 相对转动 非线性动力系统 近似解     

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

A new car-following model is proposed based on the full velocity difference model(FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau(TDGL) equation and the modified Korteweg-de Vries(mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.     

Traffic flow prediction based on BILSTM model and data denoising scheme

Accurate prediction of road traffic flow is a significant part in the intelligent transportation systems. Accurate prediction can alleviate traffic congestion, and reduce environmental pollution. For the management department, it can make effective use of road resources. For individuals, it can help people plan their own travel paths, avoid congestion, and save time. Owing to complex factors on the road, such as damage to the detector and disturbances from environment, the measured traffic volume can contain noise. Reducing the influence of noise on traffic flow prediction is a piece of very important work. Therefore, in this paper we propose a combination algorithm of denoising and BILSTM to effectively improve the performance of traffic flow prediction. At the same time, three denoising algorithms are compared to find the best combination mode. In this paper, the wavelet (WL) denoising scheme, the empirical mode decomposition (EMD) denoising scheme, and the ensemble empirical mode decomposition (EEMD) denoising scheme are all introduced to suppress outliers in traffic flow data. In addition, we combine the denoising schemes with bidirectional long short-term memory (BILSTM) network to predict the traffic flow. The data in this paper are cited from performance measurement system (PeMS). We choose three kinds of road data (mainline, off ramp, on ramp) to predict traffic flow. The results for mainline show that data denoising can improve prediction accuracy. Moreover, prediction accuracy of BILSTM+EEMD scheme is the highest in the three methods (BILSTM+WL, BILSTM+EMD, BILSTM+EEMD). The results for off ramp and on ramp show the same performance as the results for mainline. It is indicated that this model is suitable for different road sections and long-term prediction.     

An element-free Galerkin （EFG） method for numerical solution of the coupled Schrodinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrodinger-KdV equations using the elementfree Galerkin （EFG） method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method （FDM） and the finite element method （FEM）, this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.     

Stabilization strategy of a car-following model with multiple time delays of the drivers

An extended car-following model with multiple delays is constructed to describe driver's driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver's multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.     

The Stability Analysis for an Extended Car Following Model Based on Control Theory

A new method is proposed to study the stability of the car-following model considering traffic interruption probability. The stability condition for the extended ear-following model is obtained by using the Lyapunov function and the condition for no traffic jam is also given based on the control theory. Numerical simulations are conducted to demonstrate and verify the analytical results. Moreover, numerical simulations show that the traffic interruption probability has an influence on driving behavior and confirm the effectiveness of the method on the stability of traffic flow.     

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

In this paper, we analyze the generalized Camassa and Holm （CH） equation by the improved element-free Galerkin （IEFG） method. By employing the improved moving least-square （IMLS） approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.     

The element-free Galerkin method of numerically solving a regularized long-wave equation

The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.