BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alan Rendall (Johannes Gutenberg University Mainz) DTSTART:20210408T153000Z DTEND:20210408T160000Z DTSTAMP:20260421T124344Z UID:MoRN/19 DESCRIPTION:Title: Us ing Bogdanov-Takens bifurcations to study existence and stability of perio dic solutions\nby Alan Rendall (Johannes Gutenberg University Mainz) a s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nH opf bifurcations are a favourite way to prove the existence of periodic\ns olutions of a dynamical system. The aim of this talk is to describe a vari ant\nof this procedure using the less familiar concept of a Bogdanov-Taken s\nbifurcation. Surprisingly\, the latter procedure has the advantage that \nalthough the bifurcation itself is more complicated the conditions which need\nto be checked to determine the stability of the periodic solutions produced are\nmore straightforward. I will give a general discussion of th ese matters\,\nillustrating them by the example of a model for the kinase Lck. This is\nbased on work with Lisa Kreusser\, where we studied the occu rrence of\ninteresting dynamical features\, such as multistability\, perio dic solutions and\nhomoclinic loops\, in models for enzymes subject to aut ophosphorylation. I will\nalso discuss how features of this type can be li fted from smaller to larger\nreaction networks.\n LOCATION:https://researchseminars.org/talk/MoRN/19/ END:VEVENT END:VCALENDAR