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Semigroup Forum

, Volume 92, Issue 2, pp 486–493 | Cite as

Linear chaos for the Quick-Thinking-Driver model

  • J. Alberto Conejero
  • Marina Murillo-Arcila
  • Juan B. Seoane-Sepúlveda
RESEARCH ARTICLE

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.

Keywords

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

Notes

Acknowledgments

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

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • J. Alberto Conejero
    • 1
  • Marina Murillo-Arcila
    • 1
  • Juan B. Seoane-Sepúlveda
    • 2
  1. 1.Instituto Universitario de Matemática Pura y Aplicada (IUMPA)Universitat Politècnica de ValènciaValenciaSpain
  2. 2.Departamento de Análisis Matemático, Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain

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