Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

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.