Journal
NONLINEAR DYNAMICS
Volume 76, Issue 1, Pages 725-731Publisher
SPRINGER
DOI: 10.1007/s11071-013-1164-5
Keywords
Traffic flow; Lattice hydrodynamic model; KdV equation; mKdV equation
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Funding
- National Natural Science Foundation of China [11072117, 11372166, 61074142]
- Scientific Research Fund of Zhejiang Provincial, China [LY13A010005]
- Disciplinary Project of Ningbo, China [SZXL1067]
- K.C. Wong Magna Fund in Ningbo University, China
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Based on the anticipation lattice hydrodynamic models, which are described by the partial differential equations, the continuum version of the model is investigated through a reductive perturbation method. The linear stability theory is used to discuss the stability of the continuum model. The Korteweg-de Vries (for short, KdV) equation near the neutral stability line and the modified Korteweg-de Vries (for short, mKdV) equation near the critical point are obtained by using the nonlinear analysis method. And the corresponding solutions for the traffic density waves are derived, respectively. The results display that the anticipation factor has an important influence on traffic flow. From the simulation, it is shown that the traffic jam is suppressed efficiently with taking into account the anticipation effect, and the analytical result is consonant with the simulation one.
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