Systems of delay differential equations: Analysis of a model with feedback

Using topological degree theory, we prove the existence of positive periodic solutions of a system of delay differential equations for models with feedback arising on regulatory mechanisms in which self-regulation is relevant, e.g. in cell physiology. We study different models based on the cycle of testosterone and generalizations. The method in the present work allows to analyse and extend known results from a different perspective, shortening proofs and giving an alternative approach for the study of complex models.