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Multi-mode solitons in a long-short range traffic lattice model with time delay

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Abstract

We consider a new form of solutions of a special lattice model for traffic system. By analyzing nearest sites’ interactions, time delay, and bumpy effects, we deduce the bifurcation lines and surfaces for stable and unstable regions and show how they vary as parameters vary. It shows that keeping other conditions unchanged, as the incoming flow increases, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable. Besides, considering delayed optimal flow, multiple sites effect or artificial parameters can also help stabilize the traffic road condition. Moreover, by putting it into the framework of mKdV equations, we obtain the kink–antikink solitons involving all parameters, which show the feature of the traffic congestion. The result is original, and our model in differential or difference form can be reduced into the previous ones by choosing appropriate parameters. Since the optimal velocity function we considered involves finitely or infinitely many sites, the density waves can be in multi-mode and high dimension forms and can also be quasi-periodic, we show a new feature of the traffic lattice system.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No.11601232), the fundamental research funds for the Central Universities, China (Grant Nos. KJQN201717 and KYZ201537) and a Jiangsu provincial scholarship for overseas research. This work was also partially supported by the National Natural Science Foundation of China (Grant No.11775116).

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Nanjing Agricultural University, Nanjing, 210095, People’s Republic of China

    Xiufang Ren

  2. Department of Computer Science, College of Artificial Intelligence, Nanjing Agricultural University, Nanjing, 210095, People’s Republic of China

    Shiji Zhao

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  1. Xiufang Ren
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  2. Shiji Zhao
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Correspondence to Xiufang Ren.

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Ren, X., Zhao, S. Multi-mode solitons in a long-short range traffic lattice model with time delay. Nonlinear Dyn 103, 1869–1889 (2021). https://doi.org/10.1007/s11071-020-06173-6

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