BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stefan Müller (University of Vienna) DTSTART:20251023T150000Z DTEND:20251023T153000Z DTSTAMP:20260421T124651Z UID:MoRN/130 DESCRIPTION:Title: E xistence\, uniqueness\, and stability of equilibria in (generalized) mass- action systems\nby Stefan Müller (University of Vienna) as part of Se minar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe report on several recent results for reaction networks with (generalized) mass-actio n kinetics\, short (G)MAK.\n\n1. In the setting of MAK\, complex-balanced equilibria are asymptotically stable. We further clarify the binomial stru cture of mass-action systems\, and extend the stability result to 'binomia l differential inclusions'\, a very general class of dynamical systems.\n\ n2. For GMAK\, complex-balanced equilibria need not be stable. We provide sufficient (sign) conditions for linear stability.\n\nFor both results\, w e use a new decomposition of the graph Laplacian and monomial evaluation o rders (inducing 'banana' regions or 'wedges' in log coordinates).\n\nFor t wo more results\, we use our new framework for parametrized systems of gen eralized polynomial equations\, which covers equilibria of reaction networ ks with (G)MAK.\n\n3. In full generality\, we characterize the unique exis tence of solutions for all parameters. As a sufficient condition\, we prov ide a 'genuine' multivariate Descartes rule of signs.\n\n4. For MAK\, we e xtend the deficiency one theorem (from deficiency one to *dependency* one and from single to multiple terminal linkage classes).\n\nThis is joint wo rk with Georg Regensburger and Abhishek Deshpande.\n LOCATION:https://researchseminars.org/talk/MoRN/130/ END:VEVENT END:VCALENDAR