title: Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.
abstract: Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.
authors.affiliation: Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages" (UNS-CONICET), Departamento de Ingeniería Eléctrica y de Computadoras, Universidad Nacional del Sur, Avda. Alem 1253, B8000CPB Bahía Blanca, Argentina.
authors.forename: María Belén
authors.initials: MB
authors.lastname: D'Amico
authors.affiliation: Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages" (UNS-CONICET), Departamento de Ingeniería Eléctrica y de Computadoras, Universidad Nacional del Sur, Avda. Alem 1253, B8000CPB Bahía Blanca, Argentina.
authors.forename: Guillermo L
authors.initials: GL
authors.lastname: Calandrini