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

Abstract

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 selfregulation 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 analyze and extend known results from a different perspective, shortening proofs and giving an alternative approach for the study of complex models.

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

“…Owolabi et al (2018) studied the analytical and numerical solutions of a dynamical model comprising three species of systems using the fractional Fourier transform. Alliera and Amster (2018) used the topological degree theory and proved the existence of positive periodic solutions for a system of delay differential equations. Ablinger et al (2019) developed an algorithm to solve analytically linear systems of differential equations that factorize to first order.…”