Qualitative analysis of some models of delay differential equations

  1. Buedo-Fernández, Sebastián
Supervised by:
  1. Eduardo Liz Marzán Director
  2. Rosana Rodríguez López Director

Defence university: Universidade de Santiago de Compostela

Fecha de defensa: 29 July 2021

Committee:
  1. Carmen Núñez Chair
  2. Rodrigo López Pouso Secretary
  3. José Joaquim Martins Oliveira Committee member
Department:
  1. Department of Statistics, Mathematical Analysis and Optimisation

Type: Thesis

Abstract

This thesis concerns the study of the global dynamics of delay differential equations of the so-called production and destruction type, which find applications to the modelling of several phenomena in areas such as population growth dynamics, economics, cell production, etc. For instance, by applying tools coming from discrete dynamics, we provide sufficient conditions for the existence of globally attracting equilibria for families of scalar or multidimensional equations. Moreover, we extend some known results in the scalar non-autonomous case by the use of integral inequalities. Finally, the existence of periodic solutions is analysed in the general context of infinite delay, impulses and periodic coefficients.