Linear chaos for the Quick-Thinking-Driver model
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.
KeywordsDeath model Birth-and-death problem Car-following Quick-Thinking-Driver Devaney chaos Distributional chaos \(C_0\)-semigroups
The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.
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