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Linear chaos for the Quick-Thinking-Driver model

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Abstract

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

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Acknowledgments

The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politècnica de València, Edificio 8G, 46022, Valencia, Spain

    J. Alberto Conejero & Marina Murillo-Arcila

  2. Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain

    Juan B. Seoane-Sepúlveda

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  1. J. Alberto Conejero
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  2. Marina Murillo-Arcila
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  3. Juan B. Seoane-Sepúlveda
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Correspondence to J. Alberto Conejero.

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Communicated by Abdelaziz Rhandi.

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Conejero, J.A., Murillo-Arcila, M. & Seoane-Sepúlveda, J.B. Linear chaos for the Quick-Thinking-Driver model. Semigroup Forum 92, 486–493 (2016). https://doi.org/10.1007/s00233-015-9704-6

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