title: Modeling a bus through a sequence of traffic lights.
abstract: We propose a model of a bus traveling through a sequence of traffic lights, which is required to stop between the traffic signals to pick up passengers. A two dimensional model, of velocity and traveled time at each traffic light, is constructed, which shows non-trivial and chaotic behaviors for realistic city traffic parameters. We restrict the parameter values where these non-trivial and chaotic behaviors occur, by following analytically and numerically the fixed points and period 2 orbits. We define conditions where chaos may arise by determining regions in parameter space where the maximum Lyapunov exponent is positive. Chaos seems to occur as long as the ratio of the braking and accelerating capacities are greater than about ∼3.
authors.affiliation: Facultad de Ciencias Naturales y Matemáticas, Universidad de Ibagué, Ibagué, Colombia.
authors.forename: Jorge
authors.initials: J
authors.lastname: Villalobos
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
authors.forename: Víctor
authors.initials: V
authors.lastname: Muñoz
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
authors.forename: José
authors.initials: J
authors.lastname: Rogan
authors.affiliation: Departamento de Ingeniería Industrial, Universidad de los Andes, Bogotá, Colombia.
authors.forename: Roberto
authors.initials: R
authors.lastname: Zarama
authors.affiliation: Departamento de Ingeniería Industrial, Universidad de los Andes, Bogotá, Colombia.
authors.forename: Juan Felipe
authors.initials: JF
authors.lastname: Penagos
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
authors.forename: Benjamín
authors.initials: B
authors.lastname: Toledo
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
authors.forename: Juan Alejandro
authors.initials: JA
authors.lastname: Valdivia