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Linear chaos for the Quick-Thinking-Driver model

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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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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  • DOI: https://doi.org/10.1007/s00233-015-9704-6

Keywords

  • Death model
  • Birth-and-death problem
  • Car-following
  • Quick-Thinking-Driver
  • Devaney chaos
  • Distributional chaos
  • \(C_0\)-semigroups