Qualitative analysis of some models of delay differential equations
- Eduardo Liz Marzán Doktorvater/Doktormutter
- Rosana Rodríguez López Doktormutter
Universität der Verteidigung: Universidade de Santiago de Compostela
Fecha de defensa: 29 von Juli von 2021
- Carmen Núñez Präsident/in
- Rodrigo López Pouso Sekretär
- José Joaquim Martins Oliveira Vocal
Art: Dissertation
Zusammenfassung
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.