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Research Papers

Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

[+] Author and Article Information
Jianzhong Chen

College of Automation,
Northwestern Polytechnical University,
Xi'an, Shaanxi 710072, China
e-mail: jzhchen@nwpu.edu.cn

Zhongke Shi, Lei Yu, Zhiyuan Peng

College of Automation,
Northwestern Polytechnical University,
Xi'an, Shaanxi 710072, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 22, 2013; final manuscript received January 4, 2014; published online February 13, 2014. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 9(3), 031005 (Feb 13, 2014) (8 pages) Paper No: CND-13-1088; doi: 10.1115/1.4026444 History: Received April 22, 2013; Revised January 04, 2014

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

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Figures

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Fig. 1

The phase diagram in parameter space (ρ, a) for m = 3 with different values of td

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Fig. 2

The phase diagram in parameter space (ρ, a) for different values of m with td=0.3

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Fig. 3

Space-time evolutions of the density after t = 10,000 (a) td=0.0 (b) td = 0.2 (c) td = 0.4 (d) td = 0.6

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Fig. 4

Density profiles of the density waves at t = 10300 (a) td=0.0 (b) td = 0.2 (c) td = 0.4 (d) td = 0.6

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Fig. 5

Space-time evolutions of the density after t = 10,000 (a) m = 1 (b) m = 2 (c) m = 3 (d) m = 5

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Fig. 6

Density profiles of the density waves at t = 10,300 (a) m = 1 (b) m = 2 (c) m = 3 (d) m = 5

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Fig. 7

The critical sensitivity ac against td

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Fig. 8

The amplitude C of the kink-antikink soliton against td

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