Stabilization analysis and modified KdV equation of a car-following model with consideration of self-stabilizing control in historical traffic data

Nonlinear Dynamics - In this paper, an extended car-following model which depends not only on the difference of the optimal velocity and the current velocity but also on self-stabilizing control is...     

A traffic flow model considering influence of car-following and its echo characteristics

Taking into account the driving characteristics of vehicles following the vehicle in front on the imported lane of urban signalized intersections, we introduce the acceleration parameters of the vehicle and consider the queue length and volatility of the acceleration that have been affected by the time of fixed signal cycles in the mixed traffic flow. Thereby, we obtain a mixed traffic flow cellular automaton model with the effect of acceleration on the imported lane. Through analyzing the results of numerical simulation, it is found that the maximum queue length and the volatility of acceleration have a great influence on the intersection lane mixed traffic flow with the different time of fixed signal cycles and considerably on traffic arriving strength within a certain range. When the intensity is in specific range, the longer the fixed signal cycle, the shorter the maximum queue length, and the greater the volatility of acceleration, which has smaller queue jam affecting the intersection lane mixed traffic flow. Meanwhile, the improved model can reproduce the evolution and propagation characteristics of gathering–dissipating of the traffic wave in the intersection lane mixed traffic flow.     

Empirical test of a microscopic three-phase traffic theory

A review of dynamic nonlinear features of spatiotemporal congested patterns in freeway traffic is presented. The basis of the review is a comparison of theoretical features of the congested patterns that are shown by a microscopic traffic flow model in the context of the Kerner's three-phase traffic theory and empirical microscopic and macroscopic pattern characteristics measured on different freeways over various days and years. In this test of the microscopic three-phase traffic flow theory, a model of an "open" road is applied: Empirical time-dependence of traffic demand and drivers' destinations are used at the upstream model boundaries. At downstream model boundary conditions for vehicle freely leaving a modeling freeway section(s) are given. Spatiotemporal congested patterns emerge, develop, and dissolve in this open freeway model with the same types of bottlenecks as those in empirical observations. It is found that microscopic three-phase traffic models can explain all known macroscopic and microscopic empirical congested pattern features (e.g., probabilistic breakdown phenomenon as a first-order phase transition from free flow to synchronized flow, moving jam emergence in synchronized flow rather than in free flow, spatiotemporal features of synchronized flow and general congested patterns at freeway bottlenecks, intensification of downstream congestion due to upstream congestion at adjacent bottlenecks). It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic behavior is qualitatively different. Model performance with respect to spatiotemporal pattern emergence and evolution cannot be tested using these traffic characteristics. The reason for this is that important spatiotemporal features of congested traffic patterns are lost in these and many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models. PACS: 89.40. + k, 47.54. + r, 64.60.Cn, 64.60.Lx     

Relative velocity difference model for the car-following theory

To explore and evaluate the impacts of relative velocity difference (RVD) with memory on the dynamic characteristics and fuel economy of traffic flow in the intelligent transportation environment, we first analyze the linkage between RVD with different-step memory and the following car’s behaviors with the measured car-following (CF) data in cities by using the gray correlation analysis method and then present a RVD model based on the previous CF models in the literatures and calibrate it. Finally, we conduct several numerical simulations in the adaptive cruise control (ACC) strategy to explore how RVD with memory affects car’s velocity fluctuation and fuel consumptions, and find that the RVD model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that considering RVD with memory in modeling CF behaviors and designing the advanced ACC strategy can improve the stability and fuel economy of traffic flow.     

Nonlinear stability analysis of a disk brake model

It has become commonly accepted by scientists and engineers that brake squeal is generated by friction-induced self-excited vibrations of the brake system. The noise-free configuration of the brake system loses stability through a flutter-type instability and the system starts oscillating in a limit cycle. Usually, the stability analysis of disk brake models, both analytical as well as finite element based, investigates the linearized models, i.e. the eigenvalues of the linearized equations of motion. However, there are experimentally observed effects not covered by these analyses, even though the full nonlinear models include these effects in principle. The present paper describes the nonlinear stability analysis of a realistic disk brake model with 12 degrees of freedom. Using center manifold theory and artificially increasing the degree of degeneracy of the occurring bifurcation, an analytical expression for the turning points in the bifurcation diagram of the subcritical Hopf bifurcations is calculated. The parameter combination corresponding to the turning points is considered as the practical stability boundary of the system. Basic phenomena known from the operating experience of brake systems tending to squeal problems can be explained on the basis of the practical stability boundary.     

On the stability of the solution to a gonorrhea discrete mathematical model

ＯＮＴＨＥＳＴＡＢＩＬＩＴＹＯＦＴＨＥＳＯＬＵＴＩＯＮＴＯＡＧＯＮＯＲＲＨＥＡＤＩＳＣＲＥＴＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＪｉｎＪｕｎ（金均）（ＳｈａｎｇｈａｉＴｅａｃｈｅｒｓＵｎｉｖｅｒｓｉｔｙ,Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＭａｒｃｈ...     

Phase-plane analysis of conserved higher-order traffic flow model

The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.     

A car-following model with the anticipation effect of potential lane changing

In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.     

A new car-following model with consideration of inter-vehicle communication

In this paper, we construct a new car-following model with inter-vehicle communication (IVC) to study the driving behavior under an accident. The numerical results show that the proposed model can qualitatively describe the effects of IVC on each vehicle’s speed, acceleration, movement trail, and headway under an accident and that the new model can overcome the full velocity difference (FVD) model’s shortcoming that collisions occur under an accident, which illustrates that the new model can better describe the driving behavior under an accident than the FVD model.     

Non-lane-discipline-based car-following model incorporating the electronic throttle dynamics under connected environment

We investigate the nonlinear dynamics of a system of generalized Duffing-type MEMS resonator in the frame of simple analog electronic circuit. A mathematical model formed for the proposed generalized Duffing-type MEMS oscillator in which nonlinearities arising out of two different sources such as mid-plane stretching and electrostatic force can lead to variety of nonlinear phenomena such as period-doubling route, transient chaos and homo-/heteroclinic oscillations. These phenomena were confirmed through detailed numerical investigations such as phase portraits, bifurcation diagram, Poincaré map, Lyapunov exponent spectrum and finite-time Lyapunov exponent. The analog circuit realization for the Duffing-type MEMS resonator is constructed. The numerically simulated results are confirmed in the laboratory experimental observations which are closely matched with each other. The experimentally observed chaotic attractor confirmed through FFT spectrum, 0–1 test and Poincaré cross section. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio.     

On the stability of multi-layered fluids. Part I: analysis

The linear stability of the Poiseuille flow of multi-layered different fluids, described mathematically by a system of Orr-Somerfeld differential equations, is investigated. A spectral method is used to rewrite this system into a generalized eigenvalue problem, which can be solved with the QZ-algorithm. Special attention is paid to the tractibility of the interfacial conditions of the stability problem. Since we will limit ourselves to a linear stability analysis, the analytical treatment of the interfacial conditions is simplified. Some results related to simple flow configurations are presented. The origin of certain regions of interfacial instability is explained by simple analytical reasoning.