Periodic n dimensional first order coupled systems and periodic schizophrenia phenomena

Abstract

This paper introduces some existence and location results for periodic solutions of first-order coupled nonlinear systems of n ordinary differential equations. The arguments used are based on the Arzèla-Ascoli theorem and Schauder's fixed point theorem, combined with the upper and lower solution technique. To illustrate the applicability of these problems, an application to a mathematical model of the thyroid-pituitary interaction and their homeostatic mechanism is included, for specific cases of periodic events, such as relapsing catatonia.