Philipp Manfred Getto

Universidad de Castilla-La Mancha

Salón de Grados, Edificio Politécnico, 10:00h.

The talk is joint work with Torsten Lindström from Umea (S). We analyze a two-component system of differential equations with time delay. The components represent populations of respectively stem and mature cells that interact via maturation and signaling; the delay represents maturation duration. The system features a zero and a positive equilibrium. One aim is to analyze under which parameter conditions which initial histories tend to which equilibrium and if they tend to any. To analyze these questions, using an approach by Horst Thieme and collaborators,  the system will be transformed into a non-autonomous, i.e. explicitly time dependent, system. The latter is asymptotically autonomous, i.e. converges for large times to a limit system that is again autonomous, and the limit system is simpler than the original system. For the limit system, a global equilibrium analysis, that carries over to the original system, can be performed. I will try to summarize this approach and to touch on further tools such as linearization, population persistence and ultimate boundedness.