Bifurcation analysis of a class of `car following' traffic models

DOI10.1016/j.physd.2004.07.008zbMath1068.34038OpenAlexW2046861029MaRDI QIDQ1888056

Yanyan Li

Publication date: 22 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.07.008

zbMATH Keywords

Hopf bifurcationtraffic modelnonlinear system of ODEs

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (25)

Modeling vehicular traffic networks. I. ⋮ Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference ⋮ Optimization of vehicle structural parameters considering stability improvement ⋮ Bifurcation analysis and control strategy for a car-following model considering jerk behavior ⋮ Subcritical Hopf bifurcations in a car-following model with reaction-time delay ⋮ Optimal velocity functions for car-following models ⋮ Numerical bifurcation analysis of a ?car-following? model ⋮ Coarse analysis of collective behaviors: bifurcation analysis of the optimal velocity model for traffic jam formation ⋮ Analytic solutions for a functional differential equation related to a traffic flow model ⋮ Impact of driving prediction on headway and velocity in car-following model under V2X environment ⋮ Dynamical analysis of an optimal velocity model with time-delayed feedback control ⋮ Asymptotic stability analysis of binary heterogeneous traffic based on car-following model ⋮ Forecasting traffic time series with multivariate predicting method ⋮ Nonlinear network modes in cyclic systems with applications to connected vehicles ⋮ Nonlinear analysis of traffic time series at different temporal scales ⋮ On pattern formation in a class of traffic models ⋮ Continuation of oscillatory patterns in a road traffic model of three cars ⋮ A traffic flow model with overtaking as a Filippov system ⋮ Chaos analysis and delayed-feedback control in a discrete dynamic coupled map traffic model ⋮ Bifurcations and multiple traffic jams in a car-following model with reaction-time delay ⋮ Synchronization transition and traffic congestion in one-dimensional traffic model ⋮ The traffic problem: Modeling of the overtaking ⋮ One-parametric bifurcation analysis of data-driven car-following models ⋮ Stability, convergence and Hopf bifurcation analyses of the classical car-following model ⋮ Nonlinear dynamics of traffic jams

Cites Work

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• Elements of applied bifurcation theory.
• Structure stability of congestion in traffic dynamics
• Analysis of a continuous car-following model for a bus route: Existence, stability and bifurcations of synchronous motions
• Synchronized flow as a new traffic phase and related problems for traffic flow modelling
• Mathematical models for vehicular traffic
• Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
• On kinematic waves II. A theory of traffic flow on long crowded roads

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